| [ |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": -0.44967, |
| "lon": -76.99724, |
| "name": "Puerto Francisco de Orellana" |
| }, |
| { |
| "lat": 5.33573, |
| "lon": -72.3939, |
| "name": "Yopal" |
| }, |
| { |
| "lat": 9.03934, |
| "lon": -69.73364, |
| "name": "Guanare" |
| }, |
| { |
| "lat": 10.31899, |
| "lon": -65.97751, |
| "name": "Río Chico" |
| }, |
| { |
| "lat": 6.24924, |
| "lon": -57.51578, |
| "name": "New Amsterdam" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1006342.34, |
| "perimeter_km": 5084.88, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Puerto Francisco de Orellana: (-0.4497°, -76.9972°)", |
| " Yopal: (5.3357°, -72.3939°)", |
| " Guanare: (9.0393°, -69.7336°)", |
| " Río Chico: (10.3190°, -65.9775°)", |
| " New Amsterdam: (6.2492°, -57.5158°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5084.88 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1006342.34 km²", |
| "FINAL ANSWER: Area: 1006342.34 km², Perimeter: 5084.88 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": -38.15912, |
| "lon": 145.93118, |
| "name": "Warragul" |
| }, |
| { |
| "lat": -37.91667, |
| "lon": 145.11667, |
| "name": "Clayton" |
| }, |
| { |
| "lat": -33.28397, |
| "lon": 149.10018, |
| "name": "Orange" |
| }, |
| { |
| "lat": -26.66008, |
| "lon": 153.09953, |
| "name": "Maroochydore" |
| }, |
| { |
| "lat": -34.06251, |
| "lon": 151.14961, |
| "name": "Cronulla" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 173622.32, |
| "perimeter_km": 3033.12, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Warragul: (-38.1591°, 145.9312°)", |
| " Clayton: (-37.9167°, 145.1167°)", |
| " Orange: (-33.2840°, 149.1002°)", |
| " Maroochydore: (-26.6601°, 153.0995°)", |
| " Cronulla: (-34.0625°, 151.1496°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3033.12 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 173622.32 km²", |
| "FINAL ANSWER: Area: 173622.32 km², Perimeter: 3033.12 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 37.29167, |
| "lon": 127.50778, |
| "name": "Pubal" |
| }, |
| { |
| "lat": 38.42194, |
| "lon": 140.30833, |
| "name": "Yachi" |
| }, |
| { |
| "lat": 35.38329, |
| "lon": 139.93254, |
| "name": "Kisarazu" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 190343.84, |
| "perimeter_km": 2601.49, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Pubal: (37.2917°, 127.5078°)", |
| " Yachi: (38.4219°, 140.3083°)", |
| " Kisarazu: (35.3833°, 139.9325°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2601.49 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 190343.84 km²", |
| "FINAL ANSWER: Area: 190343.84 km², Perimeter: 2601.49 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": 37.06217, |
| "lon": 114.49272, |
| "name": "Xingtai" |
| }, |
| { |
| "lat": 37.80822, |
| "lon": 120.75908, |
| "name": "Dengzhou" |
| }, |
| { |
| "lat": 35.94389, |
| "lon": 126.95444, |
| "name": "Iksan" |
| }, |
| { |
| "lat": 35.37111, |
| "lon": 139.22361, |
| "name": "Hadano" |
| }, |
| { |
| "lat": 33.5547, |
| "lon": 131.72796, |
| "name": "Kunisaki" |
| }, |
| { |
| "lat": 32.84111, |
| "lon": 130.04306, |
| "name": "Isahaya" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 638976.1, |
| "perimeter_km": 4640.14, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Xingtai: (37.0622°, 114.4927°)", |
| " Dengzhou: (37.8082°, 120.7591°)", |
| " Iksan: (35.9439°, 126.9544°)", |
| " Hadano: (35.3711°, 139.2236°)", |
| " Kunisaki: (33.5547°, 131.7280°)", |
| " Isahaya: (32.8411°, 130.0431°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4640.14 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 638976.10 km²", |
| "FINAL ANSWER: Area: 638976.10 km², Perimeter: 4640.14 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": -32.48463, |
| "lon": -58.23217, |
| "name": "Concepción del Uruguay" |
| }, |
| { |
| "lat": -24.00306, |
| "lon": -53.70417, |
| "name": "Iporã" |
| }, |
| { |
| "lat": -19.98639, |
| "lon": -44.42778, |
| "name": "Mateus Leme" |
| }, |
| { |
| "lat": -23.52917, |
| "lon": -47.13528, |
| "name": "São Roque" |
| }, |
| { |
| "lat": -23.56786, |
| "lon": -46.54599, |
| "name": "Vila Formosa" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 466885.94, |
| "perimeter_km": 4154.53, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Concepción del Uruguay: (-32.4846°, -58.2322°)", |
| " Iporã: (-24.0031°, -53.7042°)", |
| " Mateus Leme: (-19.9864°, -44.4278°)", |
| " São Roque: (-23.5292°, -47.1353°)", |
| " Vila Formosa: (-23.5679°, -46.5460°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4154.53 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 466885.94 km²", |
| "FINAL ANSWER: Area: 466885.94 km², Perimeter: 4154.53 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 30.47797, |
| "lon": 91.1055, |
| "name": "Damxung" |
| }, |
| { |
| "lat": 34.8975, |
| "lon": 105.18639, |
| "name": "Dashi" |
| }, |
| { |
| "lat": 34.98756, |
| "lon": 106.20902, |
| "name": "Zhangjiachuan" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 11614.91, |
| "perimeter_km": 2995.75, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Damxung: (30.4780°, 91.1055°)", |
| " Dashi: (34.8975°, 105.1864°)", |
| " Zhangjiachuan: (34.9876°, 106.2090°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2995.75 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 11614.91 km²", |
| "FINAL ANSWER: Area: 11614.91 km², Perimeter: 2995.75 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 23.58645, |
| "lon": 56.53969, |
| "name": "Yanqul" |
| }, |
| { |
| "lat": 31.34082, |
| "lon": 69.4493, |
| "name": "Zhob" |
| }, |
| { |
| "lat": 24.85822, |
| "lon": 69.40153, |
| "name": "Naukot" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 473938.53, |
| "perimeter_km": 3568.43, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Yanqul: (23.5864°, 56.5397°)", |
| " Zhob: (31.3408°, 69.4493°)", |
| " Naukot: (24.8582°, 69.4015°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3568.43 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 473938.53 km²", |
| "FINAL ANSWER: Area: 473938.53 km², Perimeter: 3568.43 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 10.11135, |
| "lon": -63.09985, |
| "name": "Caripito" |
| }, |
| { |
| "lat": 5.86638, |
| "lon": -55.16682, |
| "name": "Paramaribo" |
| }, |
| { |
| "lat": -10.22306, |
| "lon": -54.97972, |
| "name": "Peixoto de Azevedo" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 783444.58, |
| "perimeter_km": 5214.84, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Caripito: (10.1113°, -63.0999°)", |
| " Paramaribo: (5.8664°, -55.1668°)", |
| " Peixoto de Azevedo: (-10.2231°, -54.9797°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5214.84 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 783444.58 km²", |
| "FINAL ANSWER: Area: 783444.58 km², Perimeter: 5214.84 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": -26.63222, |
| "lon": -48.68472, |
| "name": "Barra Velha" |
| }, |
| { |
| "lat": -20.94944, |
| "lon": -48.47917, |
| "name": "Bebedouro" |
| }, |
| { |
| "lat": -15.0725, |
| "lon": -57.18111, |
| "name": "Barra do Bugres" |
| }, |
| { |
| "lat": -9.56722, |
| "lon": -48.39167, |
| "name": "Miracema do Tocantins" |
| }, |
| { |
| "lat": -12.74083, |
| "lon": -38.62083, |
| "name": "Madre de Deus" |
| }, |
| { |
| "lat": -23.3075, |
| "lon": -47.13278, |
| "name": "Cabreúva" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 2294286.55, |
| "perimeter_km": 5897.25, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Barra Velha: (-26.6322°, -48.6847°)", |
| " Bebedouro: (-20.9494°, -48.4792°)", |
| " Barra do Bugres: (-15.0725°, -57.1811°)", |
| " Miracema do Tocantins: (-9.5672°, -48.3917°)", |
| " Madre de Deus: (-12.7408°, -38.6208°)", |
| " Cabreúva: (-23.3075°, -47.1328°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5897.25 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 2294286.55 km²", |
| "FINAL ANSWER: Area: 2294286.55 km², Perimeter: 5897.25 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": 37.10415, |
| "lon": -113.58412, |
| "name": "Saint George" |
| }, |
| { |
| "lat": 42.49999, |
| "lon": -96.40031, |
| "name": "Sioux City" |
| }, |
| { |
| "lat": 44.73191, |
| "lon": -93.21772, |
| "name": "Apple Valley" |
| }, |
| { |
| "lat": 43.63552, |
| "lon": -79.50113, |
| "name": "Stonegate-Queensway" |
| }, |
| { |
| "lat": 42.99812, |
| "lon": -78.18752, |
| "name": "Batavia" |
| }, |
| { |
| "lat": 38.47841, |
| "lon": -82.63794, |
| "name": "Ashland" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1390925.36, |
| "perimeter_km": 6503.38, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Saint George: (37.1041°, -113.5841°)", |
| " Sioux City: (42.5000°, -96.4003°)", |
| " Apple Valley: (44.7319°, -93.2177°)", |
| " Stonegate-Queensway: (43.6355°, -79.5011°)", |
| " Batavia: (42.9981°, -78.1875°)", |
| " Ashland: (38.4784°, -82.6379°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 6503.38 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1390925.36 km²", |
| "FINAL ANSWER: Area: 1390925.36 km², Perimeter: 6503.38 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": 18.54326, |
| "lon": -92.6453, |
| "name": "Frontera" |
| }, |
| { |
| "lat": 35.61452, |
| "lon": -88.81395, |
| "name": "Jackson" |
| }, |
| { |
| "lat": 34.02316, |
| "lon": -84.36159, |
| "name": "Roswell" |
| }, |
| { |
| "lat": 38.92567, |
| "lon": -77.02942, |
| "name": "Columbia Heights" |
| }, |
| { |
| "lat": 40.8601, |
| "lon": -73.9093, |
| "name": "University Heights" |
| }, |
| { |
| "lat": 28.54944, |
| "lon": -81.77285, |
| "name": "Clermont" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1272916.78, |
| "perimeter_km": 6685.98, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Frontera: (18.5433°, -92.6453°)", |
| " Jackson: (35.6145°, -88.8140°)", |
| " Roswell: (34.0232°, -84.3616°)", |
| " Columbia Heights: (38.9257°, -77.0294°)", |
| " University Heights: (40.8601°, -73.9093°)", |
| " Clermont: (28.5494°, -81.7729°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 6685.98 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1272916.78 km²", |
| "FINAL ANSWER: Area: 1272916.78 km², Perimeter: 6685.98 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 16.36554, |
| "lon": -92.37063, |
| "name": "Las Rosas" |
| }, |
| { |
| "lat": 38.83494, |
| "lon": -90.28511, |
| "name": "Old Jamestown" |
| }, |
| { |
| "lat": 33.88399, |
| "lon": -84.51438, |
| "name": "Smyrna" |
| }, |
| { |
| "lat": 23.0881, |
| "lon": -82.3597, |
| "name": "Diez de Octubre" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1453148.64, |
| "perimeter_km": 5766.45, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Las Rosas: (16.3655°, -92.3706°)", |
| " Old Jamestown: (38.8349°, -90.2851°)", |
| " Smyrna: (33.8840°, -84.5144°)", |
| " Diez de Octubre: (23.0881°, -82.3597°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5766.45 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1453148.64 km²", |
| "FINAL ANSWER: Area: 1453148.64 km², Perimeter: 5766.45 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": 29.61972, |
| "lon": 31.2575, |
| "name": "Al ‘Ayyāţ" |
| }, |
| { |
| "lat": 30.22886, |
| "lon": 31.48149, |
| "name": "Al-'Ubūr" |
| }, |
| { |
| "lat": 31.20864, |
| "lon": 31.63528, |
| "name": "Az Zarqā" |
| }, |
| { |
| "lat": 14.03493, |
| "lon": 35.38344, |
| "name": "Al Qadarif" |
| }, |
| { |
| "lat": 17.59898, |
| "lon": 33.97205, |
| "name": "Ed Damer" |
| }, |
| { |
| "lat": 16.6915, |
| "lon": 33.4341, |
| "name": "Shendi" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 174115.11, |
| "perimeter_km": 4123.2, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Al ‘Ayyāţ: (29.6197°, 31.2575°)", |
| " Al-'Ubūr: (30.2289°, 31.4815°)", |
| " Az Zarqā: (31.2086°, 31.6353°)", |
| " Al Qadarif: (14.0349°, 35.3834°)", |
| " Ed Damer: (17.5990°, 33.9721°)", |
| " Shendi: (16.6915°, 33.4341°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4123.20 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 174115.11 km²", |
| "FINAL ANSWER: Area: 174115.11 km², Perimeter: 4123.20 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 14.2277, |
| "lon": 121.3292, |
| "name": "Victoria" |
| }, |
| { |
| "lat": 24.07327, |
| "lon": 120.56276, |
| "name": "Chang-hua" |
| }, |
| { |
| "lat": 26.37609, |
| "lon": 127.85908, |
| "name": "Uruma" |
| }, |
| { |
| "lat": 5.82417, |
| "lon": 125.20333, |
| "name": "Glan" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1017315.13, |
| "perimeter_km": 5203.51, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Victoria: (14.2277°, 121.3292°)", |
| " Chang-hua: (24.0733°, 120.5628°)", |
| " Uruma: (26.3761°, 127.8591°)", |
| " Glan: (5.8242°, 125.2033°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5203.51 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1017315.13 km²", |
| "FINAL ANSWER: Area: 1017315.13 km², Perimeter: 5203.51 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": -38.13333, |
| "lon": 145.13333, |
| "name": "Frankston East" |
| }, |
| { |
| "lat": -37.66667, |
| "lon": 145.01667, |
| "name": "Lalor" |
| }, |
| { |
| "lat": -28.21901, |
| "lon": 152.03438, |
| "name": "Warwick" |
| }, |
| { |
| "lat": -28.11694, |
| "lon": 153.46584, |
| "name": "Palm Beach" |
| }, |
| { |
| "lat": -32.92953, |
| "lon": 151.7801, |
| "name": "Newcastle" |
| }, |
| { |
| "lat": -33.85, |
| "lon": 151.03333, |
| "name": "Auburn" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 214589.53, |
| "perimeter_km": 2826.07, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Frankston East: (-38.1333°, 145.1333°)", |
| " Lalor: (-37.6667°, 145.0167°)", |
| " Warwick: (-28.2190°, 152.0344°)", |
| " Palm Beach: (-28.1169°, 153.4658°)", |
| " Newcastle: (-32.9295°, 151.7801°)", |
| " Auburn: (-33.8500°, 151.0333°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2826.07 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 214589.53 km²", |
| "FINAL ANSWER: Area: 214589.53 km², Perimeter: 2826.07 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": -37.78247, |
| "lon": 145.31682, |
| "name": "Mooroolbark" |
| }, |
| { |
| "lat": -38.02388, |
| "lon": 144.40617, |
| "name": "Lara" |
| }, |
| { |
| "lat": -27.87683, |
| "lon": 153.28572, |
| "name": "Upper Coomera" |
| }, |
| { |
| "lat": -31.91099, |
| "lon": 152.45387, |
| "name": "Taree" |
| }, |
| { |
| "lat": -32.92953, |
| "lon": 151.7801, |
| "name": "Newcastle" |
| }, |
| { |
| "lat": -33.73333, |
| "lon": 151.0, |
| "name": "Castle Hill" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 165484.76, |
| "perimeter_km": 2865.15, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Mooroolbark: (-37.7825°, 145.3168°)", |
| " Lara: (-38.0239°, 144.4062°)", |
| " Upper Coomera: (-27.8768°, 153.2857°)", |
| " Taree: (-31.9110°, 152.4539°)", |
| " Newcastle: (-32.9295°, 151.7801°)", |
| " Castle Hill: (-33.7333°, 151.0000°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2865.15 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 165484.76 km²", |
| "FINAL ANSWER: Area: 165484.76 km², Perimeter: 2865.15 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 29.20856, |
| "lon": 105.56974, |
| "name": "Xuantan" |
| }, |
| { |
| "lat": 29.71975, |
| "lon": 106.72342, |
| "name": "Yufengshan" |
| }, |
| { |
| "lat": 32.23341, |
| "lon": 106.30126, |
| "name": "Donghe" |
| }, |
| { |
| "lat": 38.41667, |
| "lon": 126.23333, |
| "name": "Sinmak" |
| }, |
| { |
| "lat": 31.37762, |
| "lon": 120.95431, |
| "name": "Kunshan" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 845297.78, |
| "perimeter_km": 4751.23, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Xuantan: (29.2086°, 105.5697°)", |
| " Yufengshan: (29.7198°, 106.7234°)", |
| " Donghe: (32.2334°, 106.3013°)", |
| " Sinmak: (38.4167°, 126.2333°)", |
| " Kunshan: (31.3776°, 120.9543°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4751.23 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 845297.78 km²", |
| "FINAL ANSWER: Area: 845297.78 km², Perimeter: 4751.23 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": 41.43884, |
| "lon": 2.16893, |
| "name": "la Guineueta" |
| }, |
| { |
| "lat": 48.8262, |
| "lon": 2.35986, |
| "name": "Paris 13e Arrondissement" |
| }, |
| { |
| "lat": 53.22683, |
| "lon": -0.53792, |
| "name": "Lincoln" |
| }, |
| { |
| "lat": 50.58362, |
| "lon": 5.50115, |
| "name": "Seraing" |
| }, |
| { |
| "lat": 51.51312, |
| "lon": 10.25951, |
| "name": "Duderstadt" |
| }, |
| { |
| "lat": 45.95689, |
| "lon": 12.66051, |
| "name": "Pordenone" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 790990.0, |
| "perimeter_km": 3829.91, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " la Guineueta: (41.4388°, 2.1689°)", |
| " Paris 13e Arrondissement: (48.8262°, 2.3599°)", |
| " Lincoln: (53.2268°, -0.5379°)", |
| " Seraing: (50.5836°, 5.5011°)", |
| " Duderstadt: (51.5131°, 10.2595°)", |
| " Pordenone: (45.9569°, 12.6605°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3829.91 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 790990.00 km²", |
| "FINAL ANSWER: Area: 790990.00 km², Perimeter: 3829.91 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 41.06022, |
| "lon": -111.97105, |
| "name": "Layton" |
| }, |
| { |
| "lat": 41.13998, |
| "lon": -104.82025, |
| "name": "Cheyenne" |
| }, |
| { |
| "lat": 41.81392, |
| "lon": -87.61727, |
| "name": "Grand Boulevard" |
| }, |
| { |
| "lat": 33.61983, |
| "lon": -86.60888, |
| "name": "Trussville" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 995898.64, |
| "perimeter_km": 5326.7, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Layton: (41.0602°, -111.9711°)", |
| " Cheyenne: (41.1400°, -104.8203°)", |
| " Grand Boulevard: (41.8139°, -87.6173°)", |
| " Trussville: (33.6198°, -86.6089°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5326.70 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 995898.64 km²", |
| "FINAL ANSWER: Area: 995898.64 km², Perimeter: 5326.70 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 17.64344, |
| "lon": -101.55212, |
| "name": "Ixtapa-Zihuatanejo" |
| }, |
| { |
| "lat": 32.85791, |
| "lon": -97.25474, |
| "name": "Watauga" |
| }, |
| { |
| "lat": 13.66492, |
| "lon": -89.25319, |
| "name": "Antiguo Cuscatlán" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1223386.67, |
| "perimeter_km": 5417.44, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Ixtapa-Zihuatanejo: (17.6434°, -101.5521°)", |
| " Watauga: (32.8579°, -97.2547°)", |
| " Antiguo Cuscatlán: (13.6649°, -89.2532°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5417.44 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1223386.67 km²", |
| "FINAL ANSWER: Area: 1223386.67 km², Perimeter: 5417.44 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 40.83242, |
| "lon": -115.76312, |
| "name": "Elko" |
| }, |
| { |
| "lat": 48.23251, |
| "lon": -101.29627, |
| "name": "Minot" |
| }, |
| { |
| "lat": 40.5142, |
| "lon": -88.99063, |
| "name": "Normal" |
| }, |
| { |
| "lat": 35.91537, |
| "lon": -94.96996, |
| "name": "Tahlequah" |
| }, |
| { |
| "lat": 32.58847, |
| "lon": -96.95612, |
| "name": "Cedar Hill" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1896841.93, |
| "perimeter_km": 5754.15, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Elko: (40.8324°, -115.7631°)", |
| " Minot: (48.2325°, -101.2963°)", |
| " Normal: (40.5142°, -88.9906°)", |
| " Tahlequah: (35.9154°, -94.9700°)", |
| " Cedar Hill: (32.5885°, -96.9561°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5754.15 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1896841.93 km²", |
| "FINAL ANSWER: Area: 1896841.93 km², Perimeter: 5754.15 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": -30.08389, |
| "lon": -51.61611, |
| "name": "Eldorado do Sul" |
| }, |
| { |
| "lat": -23.13705, |
| "lon": -64.32426, |
| "name": "San Ramón de la Nueva Orán" |
| }, |
| { |
| "lat": -18.59222, |
| "lon": -48.705, |
| "name": "Tupaciguara" |
| }, |
| { |
| "lat": -21.97722, |
| "lon": -44.9325, |
| "name": "Caxambu" |
| }, |
| { |
| "lat": -23.54667, |
| "lon": -47.43778, |
| "name": "Votorantim" |
| }, |
| { |
| "lat": -26.23, |
| "lon": -51.08639, |
| "name": "União da Vitória" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1378083.41, |
| "perimeter_km": 4938.17, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Eldorado do Sul: (-30.0839°, -51.6161°)", |
| " San Ramón de la Nueva Orán: (-23.1370°, -64.3243°)", |
| " Tupaciguara: (-18.5922°, -48.7050°)", |
| " Caxambu: (-21.9772°, -44.9325°)", |
| " Votorantim: (-23.5467°, -47.4378°)", |
| " União da Vitória: (-26.2300°, -51.0864°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4938.17 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1378083.41 km²", |
| "FINAL ANSWER: Area: 1378083.41 km², Perimeter: 4938.17 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 44.4196, |
| "lon": 27.82536, |
| "name": "Fetești-Gară" |
| }, |
| { |
| "lat": 55.83333, |
| "lon": 37.66667, |
| "name": "Rostokino" |
| }, |
| { |
| "lat": 50.19645, |
| "lon": 39.56631, |
| "name": "Rossosh’" |
| }, |
| { |
| "lat": 43.24206, |
| "lon": 46.00013, |
| "name": "Tsotsin-Yurt" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 828686.46, |
| "perimeter_km": 4462.05, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Fetești-Gară: (44.4196°, 27.8254°)", |
| " Rostokino: (55.8333°, 37.6667°)", |
| " Rossosh’: (50.1964°, 39.5663°)", |
| " Tsotsin-Yurt: (43.2421°, 46.0001°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4462.05 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 828686.46 km²", |
| "FINAL ANSWER: Area: 828686.46 km², Perimeter: 4462.05 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": -20.03833, |
| "lon": -47.74694, |
| "name": "Igarapava" |
| }, |
| { |
| "lat": -23.44361, |
| "lon": -51.87389, |
| "name": "Sarandi" |
| }, |
| { |
| "lat": -3.72667, |
| "lon": -44.22333, |
| "name": "Pirapemas" |
| }, |
| { |
| "lat": -4.25667, |
| "lon": -43.01278, |
| "name": "Coelho Neto" |
| }, |
| { |
| "lat": -20.41278, |
| "lon": -40.68306, |
| "name": "Marechal Floriano" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1106000.54, |
| "perimeter_km": 5610.41, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Igarapava: (-20.0383°, -47.7469°)", |
| " Sarandi: (-23.4436°, -51.8739°)", |
| " Pirapemas: (-3.7267°, -44.2233°)", |
| " Coelho Neto: (-4.2567°, -43.0128°)", |
| " Marechal Floriano: (-20.4128°, -40.6831°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5610.41 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1106000.54 km²", |
| "FINAL ANSWER: Area: 1106000.54 km², Perimeter: 5610.41 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 32.27639, |
| "lon": 35.59938, |
| "name": "Kurayyimah" |
| }, |
| { |
| "lat": 32.67597, |
| "lon": 35.23986, |
| "name": "Migdal Ha‘Emeq" |
| }, |
| { |
| "lat": 41.5098, |
| "lon": 34.21414, |
| "name": "Taşköprü" |
| }, |
| { |
| "lat": 39.79803, |
| "lon": 42.67574, |
| "name": "Eleşkirt" |
| }, |
| { |
| "lat": 36.84722, |
| "lon": 40.05, |
| "name": "Ceylanpınar" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 388858.99, |
| "perimeter_km": 2832.04, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Kurayyimah: (32.2764°, 35.5994°)", |
| " Migdal Ha‘Emeq: (32.6760°, 35.2399°)", |
| " Taşköprü: (41.5098°, 34.2141°)", |
| " Eleşkirt: (39.7980°, 42.6757°)", |
| " Ceylanpınar: (36.8472°, 40.0500°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2832.04 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 388858.99 km²", |
| "FINAL ANSWER: Area: 388858.99 km², Perimeter: 2832.04 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 35.65071, |
| "lon": -78.45639, |
| "name": "Clayton" |
| }, |
| { |
| "lat": 42.90725, |
| "lon": -85.79198, |
| "name": "Jenison" |
| }, |
| { |
| "lat": 45.3001, |
| "lon": -75.91606, |
| "name": "Kanata" |
| }, |
| { |
| "lat": 42.27926, |
| "lon": -71.1495, |
| "name": "West Roxbury" |
| }, |
| { |
| "lat": 40.70038, |
| "lon": -73.59291, |
| "name": "Uniondale" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 668192.35, |
| "perimeter_km": 3337.01, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Clayton: (35.6507°, -78.4564°)", |
| " Jenison: (42.9072°, -85.7920°)", |
| " Kanata: (45.3001°, -75.9161°)", |
| " West Roxbury: (42.2793°, -71.1495°)", |
| " Uniondale: (40.7004°, -73.5929°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3337.01 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 668192.35 km²", |
| "FINAL ANSWER: Area: 668192.35 km², Perimeter: 3337.01 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": -37.77988, |
| "lon": 144.92276, |
| "name": "Ascot Vale" |
| }, |
| { |
| "lat": -34.78254, |
| "lon": 138.61077, |
| "name": "Parafield Gardens" |
| }, |
| { |
| "lat": -33.28397, |
| "lon": 149.10018, |
| "name": "Orange" |
| }, |
| { |
| "lat": -34.424, |
| "lon": 150.89345, |
| "name": "Wollongong" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 268476.14, |
| "perimeter_km": 2498.54, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Ascot Vale: (-37.7799°, 144.9228°)", |
| " Parafield Gardens: (-34.7825°, 138.6108°)", |
| " Orange: (-33.2840°, 149.1002°)", |
| " Wollongong: (-34.4240°, 150.8935°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2498.54 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 268476.14 km²", |
| "FINAL ANSWER: Area: 268476.14 km², Perimeter: 2498.54 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 46.05223, |
| "lon": 125.9552, |
| "name": "Zhaodong" |
| }, |
| { |
| "lat": 46.97544, |
| "lon": 128.04804, |
| "name": "Tieli" |
| }, |
| { |
| "lat": 33.7, |
| "lon": 135.41667, |
| "name": "Asso" |
| }, |
| { |
| "lat": 31.34689, |
| "lon": 130.45612, |
| "name": "Minamikyushu" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 578858.04, |
| "perimeter_km": 4005.22, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Zhaodong: (46.0522°, 125.9552°)", |
| " Tieli: (46.9754°, 128.0480°)", |
| " Asso: (33.7000°, 135.4167°)", |
| " Minamikyushu: (31.3469°, 130.4561°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4005.22 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 578858.04 km²", |
| "FINAL ANSWER: Area: 578858.04 km², Perimeter: 4005.22 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": 5.87693, |
| "lon": -10.04964, |
| "name": "Buchanan" |
| }, |
| { |
| "lat": 13.41033, |
| "lon": -16.70815, |
| "name": "Sukuta" |
| }, |
| { |
| "lat": 14.51255, |
| "lon": -17.00447, |
| "name": "Nguékhokh" |
| }, |
| { |
| "lat": 7.80335, |
| "lon": -3.16832, |
| "name": "Tanda" |
| }, |
| { |
| "lat": 7.69385, |
| "lon": -5.03031, |
| "name": "Bouaké" |
| }, |
| { |
| "lat": 5.69775, |
| "lon": -0.32824, |
| "name": "Atsiaman" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 614137.52, |
| "perimeter_km": 4765.94, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Buchanan: (5.8769°, -10.0496°)", |
| " Sukuta: (13.4103°, -16.7081°)", |
| " Nguékhokh: (14.5125°, -17.0045°)", |
| " Tanda: (7.8034°, -3.1683°)", |
| " Bouaké: (7.6939°, -5.0303°)", |
| " Atsiaman: (5.6978°, -0.3282°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4765.94 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 614137.52 km²", |
| "FINAL ANSWER: Area: 614137.52 km², Perimeter: 4765.94 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 36.8, |
| "lon": 4.26667, |
| "name": "Timizart" |
| }, |
| { |
| "lat": 36.772, |
| "lon": 5.8982, |
| "name": "District of Taher" |
| }, |
| { |
| "lat": 35.40417, |
| "lon": 8.12417, |
| "name": "Tébessa" |
| }, |
| { |
| "lat": 32.88743, |
| "lon": 13.18733, |
| "name": "Tripoli" |
| }, |
| { |
| "lat": 34.94529, |
| "lon": 8.56789, |
| "name": "Feriana" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 22537.88, |
| "perimeter_km": 1862.66, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Timizart: (36.8000°, 4.2667°)", |
| " District of Taher: (36.7720°, 5.8982°)", |
| " Tébessa: (35.4042°, 8.1242°)", |
| " Tripoli: (32.8874°, 13.1873°)", |
| " Feriana: (34.9453°, 8.5679°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 1862.66 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 22537.88 km²", |
| "FINAL ANSWER: Area: 22537.88 km², Perimeter: 1862.66 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": -21.72444, |
| "lon": -48.10167, |
| "name": "Américo Brasiliense" |
| }, |
| { |
| "lat": -8.49694, |
| "lon": -36.94083, |
| "name": "Pedra" |
| }, |
| { |
| "lat": -9.00972, |
| "lon": -36.05833, |
| "name": "São José da Laje" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 106530.27, |
| "perimeter_km": 3919.87, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Américo Brasiliense: (-21.7244°, -48.1017°)", |
| " Pedra: (-8.4969°, -36.9408°)", |
| " São José da Laje: (-9.0097°, -36.0583°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3919.87 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 106530.27 km²", |
| "FINAL ANSWER: Area: 106530.27 km², Perimeter: 3919.87 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": -19.96778, |
| "lon": -44.19833, |
| "name": "Betim" |
| }, |
| { |
| "lat": -15.84577, |
| "lon": -47.88369, |
| "name": "Lago Sul" |
| }, |
| { |
| "lat": -3.36139, |
| "lon": -42.41778, |
| "name": "São Bernardo" |
| }, |
| { |
| "lat": -5.115, |
| "lon": -36.63444, |
| "name": "Macau" |
| }, |
| { |
| "lat": -7.73667, |
| "lon": -37.99333, |
| "name": "Princesa Isabel" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1032953.14, |
| "perimeter_km": 4626.8, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Betim: (-19.9678°, -44.1983°)", |
| " Lago Sul: (-15.8458°, -47.8837°)", |
| " São Bernardo: (-3.3614°, -42.4178°)", |
| " Macau: (-5.1150°, -36.6344°)", |
| " Princesa Isabel: (-7.7367°, -37.9933°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4626.80 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1032953.14 km²", |
| "FINAL ANSWER: Area: 1032953.14 km², Perimeter: 4626.80 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": -29.02889, |
| "lon": -51.18167, |
| "name": "Flores da Cunha" |
| }, |
| { |
| "lat": -25.78389, |
| "lon": -53.30861, |
| "name": "Salto do Lontra" |
| }, |
| { |
| "lat": -22.0175, |
| "lon": -47.89083, |
| "name": "São Carlos" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 143702.31, |
| "perimeter_km": 1955.74, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Flores da Cunha: (-29.0289°, -51.1817°)", |
| " Salto do Lontra: (-25.7839°, -53.3086°)", |
| " São Carlos: (-22.0175°, -47.8908°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 1955.74 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 143702.31 km²", |
| "FINAL ANSWER: Area: 143702.31 km², Perimeter: 1955.74 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 29.2331, |
| "lon": 56.6022, |
| "name": "Bāft" |
| }, |
| { |
| "lat": 29.45137, |
| "lon": 55.6809, |
| "name": "Sirjan" |
| }, |
| { |
| "lat": 26.02401, |
| "lon": 75.48182, |
| "name": "Todaraisingh" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 13927.14, |
| "perimeter_km": 3967.23, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Bāft: (29.2331°, 56.6022°)", |
| " Sirjan: (29.4514°, 55.6809°)", |
| " Todaraisingh: (26.0240°, 75.4818°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3967.23 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 13927.14 km²", |
| "FINAL ANSWER: Area: 13927.14 km², Perimeter: 3967.23 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 43.32686, |
| "lon": -2.98884, |
| "name": "Leioa" |
| }, |
| { |
| "lat": 42.68607, |
| "lon": 26.32558, |
| "name": "Sliven" |
| }, |
| { |
| "lat": 42.67272, |
| "lon": 21.16688, |
| "name": "Pristina" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 89459.03, |
| "perimeter_km": 4753.0, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Leioa: (43.3269°, -2.9888°)", |
| " Sliven: (42.6861°, 26.3256°)", |
| " Pristina: (42.6727°, 21.1669°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4753.00 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 89459.03 km²", |
| "FINAL ANSWER: Area: 89459.03 km², Perimeter: 4753.00 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 8.322, |
| "lon": 77.57711, |
| "name": "Pānakkudi" |
| }, |
| { |
| "lat": 24.93805, |
| "lon": 73.82392, |
| "name": "Nāthdwāra" |
| }, |
| { |
| "lat": 18.8563, |
| "lon": 82.5716, |
| "name": "Jeypore" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 713662.81, |
| "perimeter_km": 4306.58, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Pānakkudi: (8.3220°, 77.5771°)", |
| " Nāthdwāra: (24.9381°, 73.8239°)", |
| " Jeypore: (18.8563°, 82.5716°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4306.58 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 713662.81 km²", |
| "FINAL ANSWER: Area: 713662.81 km², Perimeter: 4306.58 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": -34.92866, |
| "lon": 138.59863, |
| "name": "Adelaide" |
| }, |
| { |
| "lat": -27.20338, |
| "lon": 152.95923, |
| "name": "Narangba" |
| }, |
| { |
| "lat": -41.05584, |
| "lon": 145.90375, |
| "name": "Burnie" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 738287.89, |
| "perimeter_km": 4216.8, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Adelaide: (-34.9287°, 138.5986°)", |
| " Narangba: (-27.2034°, 152.9592°)", |
| " Burnie: (-41.0558°, 145.9038°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4216.80 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 738287.89 km²", |
| "FINAL ANSWER: Area: 738287.89 km², Perimeter: 4216.80 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 6.97647, |
| "lon": -7.79834, |
| "name": "Zou" |
| }, |
| { |
| "lat": 12.81028, |
| "lon": -16.22639, |
| "name": "Bignona" |
| }, |
| { |
| "lat": 8.939, |
| "lon": 4.78227, |
| "name": "Bode Saadu" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 572294.01, |
| "perimeter_km": 4863.55, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Zou: (6.9765°, -7.7983°)", |
| " Bignona: (12.8103°, -16.2264°)", |
| " Bode Saadu: (8.9390°, 4.7823°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4863.55 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 572294.01 km²", |
| "FINAL ANSWER: Area: 572294.01 km², Perimeter: 4863.55 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 0.4, |
| "lon": 32.63333, |
| "name": "Kira" |
| }, |
| { |
| "lat": 7.70111, |
| "lon": 27.98972, |
| "name": "Wau" |
| }, |
| { |
| "lat": 9.08569, |
| "lon": 40.86708, |
| "name": "Āsbe Teferī" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 619752.36, |
| "perimeter_km": 3714.08, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Kira: (0.4000°, 32.6333°)", |
| " Wau: (7.7011°, 27.9897°)", |
| " Āsbe Teferī: (9.0857°, 40.8671°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3714.08 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 619752.36 km²", |
| "FINAL ANSWER: Area: 619752.36 km², Perimeter: 3714.08 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": -33.41665, |
| "lon": 149.5806, |
| "name": "Bathurst" |
| }, |
| { |
| "lat": -16.92366, |
| "lon": 145.76613, |
| "name": "Cairns" |
| }, |
| { |
| "lat": -27.19354, |
| "lon": 153.02631, |
| "name": "Deception Bay" |
| }, |
| { |
| "lat": -31.91099, |
| "lon": 152.45387, |
| "name": "Taree" |
| }, |
| { |
| "lat": -33.79068, |
| "lon": 150.6693, |
| "name": "Glenmore Park" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 533018.95, |
| "perimeter_km": 4141.48, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Bathurst: (-33.4166°, 149.5806°)", |
| " Cairns: (-16.9237°, 145.7661°)", |
| " Deception Bay: (-27.1935°, 153.0263°)", |
| " Taree: (-31.9110°, 152.4539°)", |
| " Glenmore Park: (-33.7907°, 150.6693°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4141.48 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 533018.95 km²", |
| "FINAL ANSWER: Area: 533018.95 km², Perimeter: 4141.48 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 22.31811, |
| "lon": 114.26994, |
| "name": "Hang Hau" |
| }, |
| { |
| "lat": 35.0616, |
| "lon": 105.79108, |
| "name": "Lianhua" |
| }, |
| { |
| "lat": 32.77856, |
| "lon": 130.74537, |
| "name": "Kotō" |
| }, |
| { |
| "lat": 23.95671, |
| "lon": 120.57608, |
| "name": "Yuanlin" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1872788.96, |
| "perimeter_km": 6015.13, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Hang Hau: (22.3181°, 114.2699°)", |
| " Lianhua: (35.0616°, 105.7911°)", |
| " Kotō: (32.7786°, 130.7454°)", |
| " Yuanlin: (23.9567°, 120.5761°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 6015.13 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1872788.96 km²", |
| "FINAL ANSWER: Area: 1872788.96 km², Perimeter: 6015.13 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": 44.84963, |
| "lon": 7.72032, |
| "name": "Carmagnola" |
| }, |
| { |
| "lat": 48.77334, |
| "lon": 2.07393, |
| "name": "Guyancourt" |
| }, |
| { |
| "lat": 53.36592, |
| "lon": -1.99986, |
| "name": "New Mills" |
| }, |
| { |
| "lat": 51.38707, |
| "lon": 7.77019, |
| "name": "Hemer" |
| }, |
| { |
| "lat": 53.944, |
| "lon": 27.7823, |
| "name": "Kalodzishchy" |
| }, |
| { |
| "lat": 40.5825, |
| "lon": 22.95028, |
| "name": "Kalamariá" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1758996.14, |
| "perimeter_km": 6126.8, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Carmagnola: (44.8496°, 7.7203°)", |
| " Guyancourt: (48.7733°, 2.0739°)", |
| " New Mills: (53.3659°, -1.9999°)", |
| " Hemer: (51.3871°, 7.7702°)", |
| " Kalodzishchy: (53.9440°, 27.7823°)", |
| " Kalamariá: (40.5825°, 22.9503°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 6126.80 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1758996.14 km²", |
| "FINAL ANSWER: Area: 1758996.14 km², Perimeter: 6126.80 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 35.52336, |
| "lon": 119.51009, |
| "name": "Heshan" |
| }, |
| { |
| "lat": 45.54558, |
| "lon": 126.95191, |
| "name": "Acheng" |
| }, |
| { |
| "lat": 36.71667, |
| "lon": 139.68333, |
| "name": "Imaichi" |
| }, |
| { |
| "lat": 36.76835, |
| "lon": 137.12572, |
| "name": "Imizu" |
| }, |
| { |
| "lat": 35.35043, |
| "lon": 139.87029, |
| "name": "Kimitsu" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1048061.97, |
| "perimeter_km": 5086.52, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Heshan: (35.5234°, 119.5101°)", |
| " Acheng: (45.5456°, 126.9519°)", |
| " Imaichi: (36.7167°, 139.6833°)", |
| " Imizu: (36.7683°, 137.1257°)", |
| " Kimitsu: (35.3504°, 139.8703°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5086.52 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1048061.97 km²", |
| "FINAL ANSWER: Area: 1048061.97 km², Perimeter: 5086.52 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 36.20005, |
| "lon": -86.51861, |
| "name": "Mount Juliet" |
| }, |
| { |
| "lat": 42.16558, |
| "lon": -88.29425, |
| "name": "Algonquin" |
| }, |
| { |
| "lat": 42.81424, |
| "lon": -73.93957, |
| "name": "Schenectady" |
| }, |
| { |
| "lat": 42.00288, |
| "lon": -71.51478, |
| "name": "Woonsocket" |
| }, |
| { |
| "lat": 40.02789, |
| "lon": -74.86905, |
| "name": "Willingboro" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 583811.39, |
| "perimeter_km": 3537.35, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Mount Juliet: (36.2000°, -86.5186°)", |
| " Algonquin: (42.1656°, -88.2943°)", |
| " Schenectady: (42.8142°, -73.9396°)", |
| " Woonsocket: (42.0029°, -71.5148°)", |
| " Willingboro: (40.0279°, -74.8691°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3537.35 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 583811.39 km²", |
| "FINAL ANSWER: Area: 583811.39 km², Perimeter: 3537.35 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": 32.44363, |
| "lon": -117.00371, |
| "name": "La Joya" |
| }, |
| { |
| "lat": 33.9938, |
| "lon": -117.75888, |
| "name": "Chino Hills" |
| }, |
| { |
| "lat": 37.69465, |
| "lon": -122.11385, |
| "name": "Ashland" |
| }, |
| { |
| "lat": 49.24966, |
| "lon": -123.11934, |
| "name": "Vancouver" |
| }, |
| { |
| "lat": 40.56217, |
| "lon": -111.92966, |
| "name": "South Jordan" |
| }, |
| { |
| "lat": 32.89953, |
| "lon": -105.96027, |
| "name": "Alamogordo" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1367150.65, |
| "perimeter_km": 5385.25, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " La Joya: (32.4436°, -117.0037°)", |
| " Chino Hills: (33.9938°, -117.7589°)", |
| " Ashland: (37.6947°, -122.1138°)", |
| " Vancouver: (49.2497°, -123.1193°)", |
| " South Jordan: (40.5622°, -111.9297°)", |
| " Alamogordo: (32.8995°, -105.9603°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5385.25 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1367150.65 km²", |
| "FINAL ANSWER: Area: 1367150.65 km², Perimeter: 5385.25 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": 37.94203, |
| "lon": 23.64619, |
| "name": "Piraeus" |
| }, |
| { |
| "lat": 47.31667, |
| "lon": 21.11667, |
| "name": "Püspökladány" |
| }, |
| { |
| "lat": 55.75378, |
| "lon": 37.81885, |
| "name": "Novogireyevo" |
| }, |
| { |
| "lat": 48.02708, |
| "lon": 40.12305, |
| "name": "Zverevo" |
| }, |
| { |
| "lat": 45.09778, |
| "lon": 43.43639, |
| "name": "Blagodarnyy" |
| }, |
| { |
| "lat": 43.16345, |
| "lon": 46.00152, |
| "name": "Avtury" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1972378.07, |
| "perimeter_km": 6096.17, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Piraeus: (37.9420°, 23.6462°)", |
| " Püspökladány: (47.3167°, 21.1167°)", |
| " Novogireyevo: (55.7538°, 37.8188°)", |
| " Zverevo: (48.0271°, 40.1230°)", |
| " Blagodarnyy: (45.0978°, 43.4364°)", |
| " Avtury: (43.1634°, 46.0015°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 6096.17 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1972378.07 km²", |
| "FINAL ANSWER: Area: 1972378.07 km², Perimeter: 6096.17 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 18.15619, |
| "lon": 83.44727, |
| "name": "Nellimarla" |
| }, |
| { |
| "lat": 15.85212, |
| "lon": 74.50447, |
| "name": "Belagavi" |
| }, |
| { |
| "lat": 21.77369, |
| "lon": 79.80513, |
| "name": "Katangi" |
| }, |
| { |
| "lat": 24.39735, |
| "lon": 98.5177, |
| "name": "Fengping" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 696111.68, |
| "perimeter_km": 5489.37, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Nellimarla: (18.1562°, 83.4473°)", |
| " Belagavi: (15.8521°, 74.5045°)", |
| " Katangi: (21.7737°, 79.8051°)", |
| " Fengping: (24.3973°, 98.5177°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5489.37 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 696111.68 km²", |
| "FINAL ANSWER: Area: 696111.68 km², Perimeter: 5489.37 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 26.35869, |
| "lon": -80.0831, |
| "name": "Boca Raton" |
| }, |
| { |
| "lat": 28.88305, |
| "lon": -81.30868, |
| "name": "DeBary" |
| }, |
| { |
| "lat": 35.88264, |
| "lon": -80.08199, |
| "name": "Thomasville" |
| }, |
| { |
| "lat": 18.47116, |
| "lon": -77.91883, |
| "name": "Montego Bay" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 185732.82, |
| "perimeter_km": 3944.79, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Boca Raton: (26.3587°, -80.0831°)", |
| " DeBary: (28.8831°, -81.3087°)", |
| " Thomasville: (35.8826°, -80.0820°)", |
| " Montego Bay: (18.4712°, -77.9188°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3944.79 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 185732.82 km²", |
| "FINAL ANSWER: Area: 185732.82 km², Perimeter: 3944.79 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": -38.11342, |
| "lon": 145.28326, |
| "name": "Cranbourne" |
| }, |
| { |
| "lat": -37.65, |
| "lon": 145.03333, |
| "name": "Epping" |
| }, |
| { |
| "lat": -27.50578, |
| "lon": 153.10236, |
| "name": "Carindale" |
| }, |
| { |
| "lat": -22.15757, |
| "lon": 166.4572, |
| "name": "Dumbéa" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 691939.66, |
| "perimeter_km": 5572.9, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Cranbourne: (-38.1134°, 145.2833°)", |
| " Epping: (-37.6500°, 145.0333°)", |
| " Carindale: (-27.5058°, 153.1024°)", |
| " Dumbéa: (-22.1576°, 166.4572°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5572.90 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 691939.66 km²", |
| "FINAL ANSWER: Area: 691939.66 km², Perimeter: 5572.90 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": -5.08917, |
| "lon": -81.11444, |
| "name": "Paita" |
| }, |
| { |
| "lat": 6.34633, |
| "lon": -75.50888, |
| "name": "Copacabana" |
| }, |
| { |
| "lat": 0.87136, |
| "lon": -77.64027, |
| "name": "Pupiales" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 39376.45, |
| "perimeter_km": 2835.67, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Paita: (-5.0892°, -81.1144°)", |
| " Copacabana: (6.3463°, -75.5089°)", |
| " Pupiales: (0.8714°, -77.6403°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2835.67 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 39376.45 km²", |
| "FINAL ANSWER: Area: 39376.45 km², Perimeter: 2835.67 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": -23.02639, |
| "lon": -45.55528, |
| "name": "Taubaté" |
| }, |
| { |
| "lat": -6.96596, |
| "lon": -35.7951, |
| "name": "Remígio" |
| }, |
| { |
| "lat": -8.75632, |
| "lon": -35.09995, |
| "name": "Tamandaré" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 170889.76, |
| "perimeter_km": 4220.94, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Taubaté: (-23.0264°, -45.5553°)", |
| " Remígio: (-6.9660°, -35.7951°)", |
| " Tamandaré: (-8.7563°, -35.0999°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4220.94 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 170889.76 km²", |
| "FINAL ANSWER: Area: 170889.76 km², Perimeter: 4220.94 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": 11.46009, |
| "lon": 78.18635, |
| "name": "Rasipuram" |
| }, |
| { |
| "lat": 8.29957, |
| "lon": 77.24062, |
| "name": "Unnamalaikadai" |
| }, |
| { |
| "lat": 10.47327, |
| "lon": 76.25577, |
| "name": "Marattakara" |
| }, |
| { |
| "lat": 15.25612, |
| "lon": 75.24735, |
| "name": "Kundgol" |
| }, |
| { |
| "lat": 23.63722, |
| "lon": 79.06275, |
| "name": "Rehli" |
| }, |
| { |
| "lat": 23.62118, |
| "lon": 85.46748, |
| "name": "Barkā Kānā" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 769497.43, |
| "perimeter_km": 4396.59, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Rasipuram: (11.4601°, 78.1864°)", |
| " Unnamalaikadai: (8.2996°, 77.2406°)", |
| " Marattakara: (10.4733°, 76.2558°)", |
| " Kundgol: (15.2561°, 75.2473°)", |
| " Rehli: (23.6372°, 79.0627°)", |
| " Barkā Kānā: (23.6212°, 85.4675°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4396.59 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 769497.43 km²", |
| "FINAL ANSWER: Area: 769497.43 km², Perimeter: 4396.59 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 34.85262, |
| "lon": -82.39401, |
| "name": "Greenville" |
| }, |
| { |
| "lat": 40.94782, |
| "lon": -90.37124, |
| "name": "Galesburg" |
| }, |
| { |
| "lat": 40.78788, |
| "lon": -74.01431, |
| "name": "West New York" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 482566.48, |
| "perimeter_km": 3334.73, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Greenville: (34.8526°, -82.3940°)", |
| " Galesburg: (40.9478°, -90.3712°)", |
| " West New York: (40.7879°, -74.0143°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3334.73 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 482566.48 km²", |
| "FINAL ANSWER: Area: 482566.48 km², Perimeter: 3334.73 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": -34.28853, |
| "lon": 146.05093, |
| "name": "Griffith" |
| }, |
| { |
| "lat": -31.9652, |
| "lon": 141.4512, |
| "name": "Broken Hill" |
| }, |
| { |
| "lat": -28.21298, |
| "lon": 153.53634, |
| "name": "Banora Point" |
| }, |
| { |
| "lat": -33.89743, |
| "lon": 150.93446, |
| "name": "Cabramatta" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 367552.59, |
| "perimeter_km": 2865.14, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Griffith: (-34.2885°, 146.0509°)", |
| " Broken Hill: (-31.9652°, 141.4512°)", |
| " Banora Point: (-28.2130°, 153.5363°)", |
| " Cabramatta: (-33.8974°, 150.9345°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2865.14 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 367552.59 km²", |
| "FINAL ANSWER: Area: 367552.59 km², Perimeter: 2865.14 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 36.61162, |
| "lon": -119.52707, |
| "name": "Parlier" |
| }, |
| { |
| "lat": 36.97412, |
| "lon": -122.0308, |
| "name": "Santa Cruz" |
| }, |
| { |
| "lat": 47.18538, |
| "lon": -122.2929, |
| "name": "Puyallup" |
| }, |
| { |
| "lat": 50.28337, |
| "lon": -107.80135, |
| "name": "Swift Current" |
| }, |
| { |
| "lat": 40.31412, |
| "lon": -112.00688, |
| "name": "Eagle Mountain" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1105498.58, |
| "perimeter_km": 4406.11, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Parlier: (36.6116°, -119.5271°)", |
| " Santa Cruz: (36.9741°, -122.0308°)", |
| " Puyallup: (47.1854°, -122.2929°)", |
| " Swift Current: (50.2834°, -107.8013°)", |
| " Eagle Mountain: (40.3141°, -112.0069°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4406.11 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1105498.58 km²", |
| "FINAL ANSWER: Area: 1105498.58 km², Perimeter: 4406.11 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 34.92889, |
| "lon": 116.46528, |
| "name": "Yucheng" |
| }, |
| { |
| "lat": 40.32306, |
| "lon": 128.65528, |
| "name": "Iwŏn-ŭp" |
| }, |
| { |
| "lat": 35.91333, |
| "lon": 128.82, |
| "name": "Hayang" |
| }, |
| { |
| "lat": 32.65, |
| "lon": 130.66667, |
| "name": "Matsubase" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 483680.8, |
| "perimeter_km": 3454.62, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Yucheng: (34.9289°, 116.4653°)", |
| " Iwŏn-ŭp: (40.3231°, 128.6553°)", |
| " Hayang: (35.9133°, 128.8200°)", |
| " Matsubase: (32.6500°, 130.6667°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3454.62 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 483680.80 km²", |
| "FINAL ANSWER: Area: 483680.80 km², Perimeter: 3454.62 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 8.54884, |
| "lon": 76.91716, |
| "name": "Sreekaryam" |
| }, |
| { |
| "lat": 23.84765, |
| "lon": 78.79903, |
| "name": "Makronia" |
| }, |
| { |
| "lat": 13.21055, |
| "lon": 79.0956, |
| "name": "Chittoor" |
| }, |
| { |
| "lat": 10.92687, |
| "lon": 79.27056, |
| "name": "Papanasam" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 186154.96, |
| "perimeter_km": 3520.1, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Sreekaryam: (8.5488°, 76.9172°)", |
| " Makronia: (23.8477°, 78.7990°)", |
| " Chittoor: (13.2105°, 79.0956°)", |
| " Papanasam: (10.9269°, 79.2706°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3520.10 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 186154.96 km²", |
| "FINAL ANSWER: Area: 186154.96 km², Perimeter: 3520.10 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": -12.05048, |
| "lon": -76.97335, |
| "name": "Santa Anita - Los Ficus" |
| }, |
| { |
| "lat": -7.05614, |
| "lon": -76.5911, |
| "name": "Bellavista" |
| }, |
| { |
| "lat": -17.39228, |
| "lon": -66.27838, |
| "name": "Quillacollo" |
| }, |
| { |
| "lat": -20.21326, |
| "lon": -70.15027, |
| "name": "Iquique" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 630329.33, |
| "perimeter_km": 3838.75, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Santa Anita - Los Ficus: (-12.0505°, -76.9733°)", |
| " Bellavista: (-7.0561°, -76.5911°)", |
| " Quillacollo: (-17.3923°, -66.2784°)", |
| " Iquique: (-20.2133°, -70.1503°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3838.75 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 630329.33 km²", |
| "FINAL ANSWER: Area: 630329.33 km², Perimeter: 3838.75 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 0.60419, |
| "lon": 29.31004, |
| "name": "Mangina" |
| }, |
| { |
| "lat": 3.03716, |
| "lon": 29.53551, |
| "name": "Watsa" |
| }, |
| { |
| "lat": 13.15611, |
| "lon": 37.89806, |
| "name": "Debark’" |
| }, |
| { |
| "lat": 8.66667, |
| "lon": 38.21667, |
| "name": "Tulu Bolo" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 374736.65, |
| "perimeter_km": 3557.94, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Mangina: (0.6042°, 29.3100°)", |
| " Watsa: (3.0372°, 29.5355°)", |
| " Debark’: (13.1561°, 37.8981°)", |
| " Tulu Bolo: (8.6667°, 38.2167°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3557.94 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 374736.65 km²", |
| "FINAL ANSWER: Area: 374736.65 km², Perimeter: 3557.94 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 32.01034, |
| "lon": 34.77918, |
| "name": "H̱olon" |
| }, |
| { |
| "lat": 31.58428, |
| "lon": 54.4428, |
| "name": "Mahrīz" |
| }, |
| { |
| "lat": 26.18872, |
| "lon": 73.02649, |
| "name": "Sāngaria" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 223374.9, |
| "perimeter_km": 7511.93, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " H̱olon: (32.0103°, 34.7792°)", |
| " Mahrīz: (31.5843°, 54.4428°)", |
| " Sāngaria: (26.1887°, 73.0265°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 7511.93 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 223374.90 km²", |
| "FINAL ANSWER: Area: 223374.90 km², Perimeter: 7511.93 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 37.7688, |
| "lon": -1.50229, |
| "name": "Totana" |
| }, |
| { |
| "lat": 40.38897, |
| "lon": -3.74569, |
| "name": "Latina" |
| }, |
| { |
| "lat": 47.36667, |
| "lon": 1.75, |
| "name": "Romorantin-Lanthenay" |
| }, |
| { |
| "lat": 53.10766, |
| "lon": 8.46322, |
| "name": "Hude" |
| }, |
| { |
| "lat": 41.00996, |
| "lon": 14.13013, |
| "name": "Casal di Principe" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1264334.99, |
| "perimeter_km": 4837.57, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Totana: (37.7688°, -1.5023°)", |
| " Latina: (40.3890°, -3.7457°)", |
| " Romorantin-Lanthenay: (47.3667°, 1.7500°)", |
| " Hude: (53.1077°, 8.4632°)", |
| " Casal di Principe: (41.0100°, 14.1301°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4837.57 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1264334.99 km²", |
| "FINAL ANSWER: Area: 1264334.99 km², Perimeter: 4837.57 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 0.69781, |
| "lon": 29.51863, |
| "name": "Hyosha" |
| }, |
| { |
| "lat": 7.31667, |
| "lon": 38.08333, |
| "name": "K’olīto" |
| }, |
| { |
| "lat": 6.8773, |
| "lon": 37.93619, |
| "name": "Badessa" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 17432.77, |
| "perimeter_km": 2411.92, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Hyosha: (0.6978°, 29.5186°)", |
| " K’olīto: (7.3167°, 38.0833°)", |
| " Badessa: (6.8773°, 37.9362°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2411.92 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 17432.77 km²", |
| "FINAL ANSWER: Area: 17432.77 km², Perimeter: 2411.92 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": -30.3875, |
| "lon": -56.45139, |
| "name": "Quaraí" |
| }, |
| { |
| "lat": -32.99835, |
| "lon": -60.76791, |
| "name": "Pérez" |
| }, |
| { |
| "lat": -16.03095, |
| "lon": -48.02929, |
| "name": "Santa Maria" |
| }, |
| { |
| "lat": -23.19361, |
| "lon": -49.38389, |
| "name": "Piraju" |
| }, |
| { |
| "lat": -28.65083, |
| "lon": -49.21, |
| "name": "Morro da Fumaça" |
| }, |
| { |
| "lat": -29.88667, |
| "lon": -50.26972, |
| "name": "Osório" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 644949.91, |
| "perimeter_km": 4965.87, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Quaraí: (-30.3875°, -56.4514°)", |
| " Pérez: (-32.9984°, -60.7679°)", |
| " Santa Maria: (-16.0310°, -48.0293°)", |
| " Piraju: (-23.1936°, -49.3839°)", |
| " Morro da Fumaça: (-28.6508°, -49.2100°)", |
| " Osório: (-29.8867°, -50.2697°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4965.87 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 644949.91 km²", |
| "FINAL ANSWER: Area: 644949.91 km², Perimeter: 4965.87 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 34.01223, |
| "lon": -117.68894, |
| "name": "Chino" |
| }, |
| { |
| "lat": 35.50672, |
| "lon": -97.76254, |
| "name": "Yukon" |
| }, |
| { |
| "lat": 30.51353, |
| "lon": -97.73973, |
| "name": "Brushy Creek" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 510382.16, |
| "perimeter_km": 4292.39, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Chino: (34.0122°, -117.6889°)", |
| " Yukon: (35.5067°, -97.7625°)", |
| " Brushy Creek: (30.5135°, -97.7397°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4292.39 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 510382.16 km²", |
| "FINAL ANSWER: Area: 510382.16 km², Perimeter: 4292.39 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": -37.89138, |
| "lon": 144.62368, |
| "name": "Wyndham Vale" |
| }, |
| { |
| "lat": -20.72523, |
| "lon": 139.49727, |
| "name": "Mount Isa" |
| }, |
| { |
| "lat": -34.03857, |
| "lon": 151.10005, |
| "name": "Miranda" |
| }, |
| { |
| "lat": -37.97695, |
| "lon": 145.25866, |
| "name": "Endeavour Hills" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 694650.52, |
| "perimeter_km": 4580.53, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Wyndham Vale: (-37.8914°, 144.6237°)", |
| " Mount Isa: (-20.7252°, 139.4973°)", |
| " Miranda: (-34.0386°, 151.1001°)", |
| " Endeavour Hills: (-37.9770°, 145.2587°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4580.53 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 694650.52 km²", |
| "FINAL ANSWER: Area: 694650.52 km², Perimeter: 4580.53 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": 13.04394, |
| "lon": 80.17251, |
| "name": "Valasaravakkam" |
| }, |
| { |
| "lat": 15.78502, |
| "lon": 80.30663, |
| "name": "Vetapālem" |
| }, |
| { |
| "lat": 20.3306, |
| "lon": 74.24467, |
| "name": "Chāndor" |
| }, |
| { |
| "lat": 28.64133, |
| "lon": 77.01415, |
| "name": "Bāprola" |
| }, |
| { |
| "lat": 23.19259, |
| "lon": 82.1272, |
| "name": "Bangawan" |
| }, |
| { |
| "lat": 17.30132, |
| "lon": 95.19833, |
| "name": "Kyonpyaw" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1710539.33, |
| "perimeter_km": 6070.89, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Valasaravakkam: (13.0439°, 80.1725°)", |
| " Vetapālem: (15.7850°, 80.3066°)", |
| " Chāndor: (20.3306°, 74.2447°)", |
| " Bāprola: (28.6413°, 77.0142°)", |
| " Bangawan: (23.1926°, 82.1272°)", |
| " Kyonpyaw: (17.3013°, 95.1983°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 6070.89 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1710539.33 km²", |
| "FINAL ANSWER: Area: 1710539.33 km², Perimeter: 6070.89 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": -37.814, |
| "lon": 144.96332, |
| "name": "Melbourne" |
| }, |
| { |
| "lat": -27.93994, |
| "lon": 153.31436, |
| "name": "Pacific Pines" |
| }, |
| { |
| "lat": -33.92893, |
| "lon": 151.05111, |
| "name": "Punchbowl" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 128116.72, |
| "perimeter_km": 2743.29, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Melbourne: (-37.8140°, 144.9633°)", |
| " Pacific Pines: (-27.9399°, 153.3144°)", |
| " Punchbowl: (-33.9289°, 151.0511°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2743.29 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 128116.72 km²", |
| "FINAL ANSWER: Area: 128116.72 km², Perimeter: 2743.29 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": -23.54015, |
| "lon": -46.48581, |
| "name": "Artur Alvim" |
| }, |
| { |
| "lat": -16.3775, |
| "lon": -39.58028, |
| "name": "Eunápolis" |
| }, |
| { |
| "lat": -17.34111, |
| "lon": -39.22083, |
| "name": "Prado" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 53377.58, |
| "perimeter_km": 2211.47, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Artur Alvim: (-23.5402°, -46.4858°)", |
| " Eunápolis: (-16.3775°, -39.5803°)", |
| " Prado: (-17.3411°, -39.2208°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2211.47 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 53377.58 km²", |
| "FINAL ANSWER: Area: 53377.58 km², Perimeter: 2211.47 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 11.31823, |
| "lon": -12.28332, |
| "name": "Labé" |
| }, |
| { |
| "lat": 14.71542, |
| "lon": -17.27334, |
| "name": "Rufisque" |
| }, |
| { |
| "lat": 11.44379, |
| "lon": -2.22548, |
| "name": "Tô" |
| }, |
| { |
| "lat": 10.33137, |
| "lon": -3.18202, |
| "name": "Gaoua" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 288236.28, |
| "perimeter_km": 3490.77, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Labé: (11.3182°, -12.2833°)", |
| " Rufisque: (14.7154°, -17.2733°)", |
| " Tô: (11.4438°, -2.2255°)", |
| " Gaoua: (10.3314°, -3.1820°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3490.77 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 288236.28 km²", |
| "FINAL ANSWER: Area: 288236.28 km², Perimeter: 3490.77 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 43.32393, |
| "lon": 5.4584, |
| "name": "Les Olives" |
| }, |
| { |
| "lat": 47.49494, |
| "lon": 8.71954, |
| "name": "Stadt Winterthur (Kreis 1)" |
| }, |
| { |
| "lat": 51.81, |
| "lon": 4.67361, |
| "name": "Dordrecht" |
| }, |
| { |
| "lat": 41.76836, |
| "lon": 26.19775, |
| "name": "Svilengrad" |
| }, |
| { |
| "lat": 42.15387, |
| "lon": 24.75001, |
| "name": "Plovdiv" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 953618.99, |
| "perimeter_km": 4765.57, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Les Olives: (43.3239°, 5.4584°)", |
| " Stadt Winterthur (Kreis 1): (47.4949°, 8.7195°)", |
| " Dordrecht: (51.8100°, 4.6736°)", |
| " Svilengrad: (41.7684°, 26.1977°)", |
| " Plovdiv: (42.1539°, 24.7500°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4765.57 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 953618.99 km²", |
| "FINAL ANSWER: Area: 953618.99 km², Perimeter: 4765.57 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": 50.32124, |
| "lon": 17.57461, |
| "name": "Prudnik" |
| }, |
| { |
| "lat": 53.18478, |
| "lon": -3.02578, |
| "name": "Hawarden" |
| }, |
| { |
| "lat": 54.15, |
| "lon": -4.48333, |
| "name": "Douglas" |
| }, |
| { |
| "lat": 59.19858, |
| "lon": 17.83317, |
| "name": "Tumba" |
| }, |
| { |
| "lat": 57.87292, |
| "lon": 39.52969, |
| "name": "Tutayev" |
| }, |
| { |
| "lat": 48.17927, |
| "lon": 40.7792, |
| "name": "Belaya Kalitva" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 2264162.15, |
| "perimeter_km": 7094.64, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Prudnik: (50.3212°, 17.5746°)", |
| " Hawarden: (53.1848°, -3.0258°)", |
| " Douglas: (54.1500°, -4.4833°)", |
| " Tumba: (59.1986°, 17.8332°)", |
| " Tutayev: (57.8729°, 39.5297°)", |
| " Belaya Kalitva: (48.1793°, 40.7792°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 7094.64 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 2264162.15 km²", |
| "FINAL ANSWER: Area: 2264162.15 km², Perimeter: 7094.64 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 49.225, |
| "lon": -123.0, |
| "name": "Metrotown" |
| }, |
| { |
| "lat": 47.14121, |
| "lon": -122.27012, |
| "name": "South Hill" |
| }, |
| { |
| "lat": 38.66879, |
| "lon": -120.98716, |
| "name": "Cameron Park" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 12024.62, |
| "perimeter_km": 2370.46, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Metrotown: (49.2250°, -123.0000°)", |
| " South Hill: (47.1412°, -122.2701°)", |
| " Cameron Park: (38.6688°, -120.9872°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2370.46 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 12024.62 km²", |
| "FINAL ANSWER: Area: 12024.62 km², Perimeter: 2370.46 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": -7.95889, |
| "lon": -79.23917, |
| "name": "Santiago de Cao" |
| }, |
| { |
| "lat": 6.17358, |
| "lon": -75.33621, |
| "name": "Marinilla" |
| }, |
| { |
| "lat": 9.31847, |
| "lon": -75.2933, |
| "name": "Corozal" |
| }, |
| { |
| "lat": -16.08333, |
| "lon": -69.66667, |
| "name": "Ilave" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1284258.44, |
| "perimeter_km": 6248.96, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Santiago de Cao: (-7.9589°, -79.2392°)", |
| " Marinilla: (6.1736°, -75.3362°)", |
| " Corozal: (9.3185°, -75.2933°)", |
| " Ilave: (-16.0833°, -69.6667°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 6248.96 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1284258.44 km²", |
| "FINAL ANSWER: Area: 1284258.44 km², Perimeter: 6248.96 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": -25.85583, |
| "lon": -52.52333, |
| "name": "Chopinzinho" |
| }, |
| { |
| "lat": -22.10809, |
| "lon": -56.53253, |
| "name": "Bela Vista" |
| }, |
| { |
| "lat": -22.90642, |
| "lon": -43.18223, |
| "name": "Rio de Janeiro" |
| }, |
| { |
| "lat": -23.63143, |
| "lon": -46.62072, |
| "name": "Cursino" |
| }, |
| { |
| "lat": -23.77806, |
| "lon": -45.35806, |
| "name": "Ilhabela" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 303501.86, |
| "perimeter_km": 3205.43, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Chopinzinho: (-25.8558°, -52.5233°)", |
| " Bela Vista: (-22.1081°, -56.5325°)", |
| " Rio de Janeiro: (-22.9064°, -43.1822°)", |
| " Cursino: (-23.6314°, -46.6207°)", |
| " Ilhabela: (-23.7781°, -45.3581°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3205.43 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 303501.86 km²", |
| "FINAL ANSWER: Area: 303501.86 km², Perimeter: 3205.43 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 6.32229, |
| "lon": 19.07922, |
| "name": "Dekoa" |
| }, |
| { |
| "lat": -1.09056, |
| "lon": 29.2925, |
| "name": "Kirumba" |
| }, |
| { |
| "lat": -2.07444, |
| "lon": 29.75667, |
| "name": "Gitarama" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 40800.63, |
| "perimeter_km": 3031.56, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Dekoa: (6.3223°, 19.0792°)", |
| " Kirumba: (-1.0906°, 29.2925°)", |
| " Gitarama: (-2.0744°, 29.7567°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3031.56 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 40800.63 km²", |
| "FINAL ANSWER: Area: 40800.63 km², Perimeter: 3031.56 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": 36.20983, |
| "lon": -5.38452, |
| "name": "San Roque" |
| }, |
| { |
| "lat": 47.7996, |
| "lon": 3.57033, |
| "name": "Auxerre" |
| }, |
| { |
| "lat": 49.38167, |
| "lon": 3.32361, |
| "name": "Soissons" |
| }, |
| { |
| "lat": 52.225, |
| "lon": 4.52222, |
| "name": "Sassenheim" |
| }, |
| { |
| "lat": 57.81922, |
| "lon": 28.33181, |
| "name": "Pskov" |
| }, |
| { |
| "lat": 37.96775, |
| "lon": 23.5721, |
| "name": "Pérama" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 3918777.0, |
| "perimeter_km": 8417.13, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " San Roque: (36.2098°, -5.3845°)", |
| " Auxerre: (47.7996°, 3.5703°)", |
| " Soissons: (49.3817°, 3.3236°)", |
| " Sassenheim: (52.2250°, 4.5222°)", |
| " Pskov: (57.8192°, 28.3318°)", |
| " Pérama: (37.9678°, 23.5721°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 8417.13 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 3918777.00 km²", |
| "FINAL ANSWER: Area: 3918777.00 km², Perimeter: 8417.13 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 52.24467, |
| "lon": 0.40418, |
| "name": "Newmarket" |
| }, |
| { |
| "lat": 52.29083, |
| "lon": 4.58333, |
| "name": "Hillegom" |
| }, |
| { |
| "lat": 48.17319, |
| "lon": 27.30075, |
| "name": "Edineţ" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 25970.06, |
| "perimeter_km": 3910.65, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Newmarket: (52.2447°, 0.4042°)", |
| " Hillegom: (52.2908°, 4.5833°)", |
| " Edineţ: (48.1732°, 27.3008°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3910.65 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 25970.06 km²", |
| "FINAL ANSWER: Area: 25970.06 km², Perimeter: 3910.65 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": -1.94995, |
| "lon": 30.05885, |
| "name": "Kigali" |
| }, |
| { |
| "lat": 1.15167, |
| "lon": 33.155, |
| "name": "Buyende" |
| }, |
| { |
| "lat": -3.13333, |
| "lon": 33.53333, |
| "name": "Malampaka" |
| }, |
| { |
| "lat": -8.9, |
| "lon": 34.58333, |
| "name": "Ilembula" |
| }, |
| { |
| "lat": -14.82027, |
| "lon": 34.63586, |
| "name": "Ntcheu" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 370425.97, |
| "perimeter_km": 3792.3, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Kigali: (-1.9500°, 30.0588°)", |
| " Buyende: (1.1517°, 33.1550°)", |
| " Malampaka: (-3.1333°, 33.5333°)", |
| " Ilembula: (-8.9000°, 34.5833°)", |
| " Ntcheu: (-14.8203°, 34.6359°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3792.30 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 370425.97 km²", |
| "FINAL ANSWER: Area: 370425.97 km², Perimeter: 3792.30 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": -37.82289, |
| "lon": 147.61041, |
| "name": "Bairnsdale" |
| }, |
| { |
| "lat": -37.83382, |
| "lon": 144.93834, |
| "name": "City of Port Phillip" |
| }, |
| { |
| "lat": -27.62329, |
| "lon": 153.04785, |
| "name": "Calamvale" |
| }, |
| { |
| "lat": -28.00274, |
| "lon": 153.42999, |
| "name": "Surfers Paradise" |
| }, |
| { |
| "lat": -33.52314, |
| "lon": 151.31325, |
| "name": "Umina Beach" |
| }, |
| { |
| "lat": -33.94185, |
| "lon": 150.8717, |
| "name": "Prestons" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 214028.34, |
| "perimeter_km": 2885.45, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Bairnsdale: (-37.8229°, 147.6104°)", |
| " City of Port Phillip: (-37.8338°, 144.9383°)", |
| " Calamvale: (-27.6233°, 153.0479°)", |
| " Surfers Paradise: (-28.0027°, 153.4300°)", |
| " Umina Beach: (-33.5231°, 151.3133°)", |
| " Prestons: (-33.9419°, 150.8717°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2885.45 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 214028.34 km²", |
| "FINAL ANSWER: Area: 214028.34 km², Perimeter: 2885.45 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": -30.71066, |
| "lon": -62.00714, |
| "name": "Morteros" |
| }, |
| { |
| "lat": -18.54389, |
| "lon": -53.12917, |
| "name": "Costa Rica" |
| }, |
| { |
| "lat": -13.03667, |
| "lon": -46.77167, |
| "name": "Campos Belos" |
| }, |
| { |
| "lat": -15.47949, |
| "lon": -44.3652, |
| "name": "Januária" |
| }, |
| { |
| "lat": -23.425, |
| "lon": -49.72083, |
| "name": "Carlópolis" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 959903.03, |
| "perimeter_km": 5418.88, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Morteros: (-30.7107°, -62.0071°)", |
| " Costa Rica: (-18.5439°, -53.1292°)", |
| " Campos Belos: (-13.0367°, -46.7717°)", |
| " Januária: (-15.4795°, -44.3652°)", |
| " Carlópolis: (-23.4250°, -49.7208°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5418.88 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 959903.03 km²", |
| "FINAL ANSWER: Area: 959903.03 km², Perimeter: 5418.88 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": -11.45528, |
| "lon": -41.43611, |
| "name": "América Dourada" |
| }, |
| { |
| "lat": -19.75, |
| "lon": -43.0375, |
| "name": "Nova Era" |
| }, |
| { |
| "lat": -1.22361, |
| "lon": -48.29444, |
| "name": "Santa Bárbara do Pará" |
| }, |
| { |
| "lat": -4.22583, |
| "lon": -38.73056, |
| "name": "Redenção" |
| }, |
| { |
| "lat": -6.22944, |
| "lon": -36.02278, |
| "name": "Santa Cruz" |
| }, |
| { |
| "lat": -14.28361, |
| "lon": -39.84278, |
| "name": "Itagibá" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1230137.85, |
| "perimeter_km": 5909.93, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " América Dourada: (-11.4553°, -41.4361°)", |
| " Nova Era: (-19.7500°, -43.0375°)", |
| " Santa Bárbara do Pará: (-1.2236°, -48.2944°)", |
| " Redenção: (-4.2258°, -38.7306°)", |
| " Santa Cruz: (-6.2294°, -36.0228°)", |
| " Itagibá: (-14.2836°, -39.8428°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5909.93 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1230137.85 km²", |
| "FINAL ANSWER: Area: 1230137.85 km², Perimeter: 5909.93 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 22.36718, |
| "lon": 114.12347, |
| "name": "Tai Wo Hau" |
| }, |
| { |
| "lat": 32.54278, |
| "lon": 111.50861, |
| "name": "Danjiangkou" |
| }, |
| { |
| "lat": 35.27814, |
| "lon": 126.51181, |
| "name": "Yeonggwang" |
| }, |
| { |
| "lat": 31.71667, |
| "lon": 130.73333, |
| "name": "Hamanoichi" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1351571.91, |
| "perimeter_km": 5075.34, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Tai Wo Hau: (22.3672°, 114.1235°)", |
| " Danjiangkou: (32.5428°, 111.5086°)", |
| " Yeonggwang: (35.2781°, 126.5118°)", |
| " Hamanoichi: (31.7167°, 130.7333°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5075.34 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1351571.91 km²", |
| "FINAL ANSWER: Area: 1351571.91 km², Perimeter: 5075.34 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": -8.07417, |
| "lon": -39.11917, |
| "name": "Salgueiro" |
| }, |
| { |
| "lat": -7.38917, |
| "lon": -38.77444, |
| "name": "Mauriti" |
| }, |
| { |
| "lat": -4.28694, |
| "lon": -38.64306, |
| "name": "Barreira" |
| }, |
| { |
| "lat": -7.59111, |
| "lon": -35.49139, |
| "name": "São Vicente Férrer" |
| }, |
| { |
| "lat": -10.7375, |
| "lon": -37.08167, |
| "name": "Maruim" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 153973.7, |
| "perimeter_km": 1698.79, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Salgueiro: (-8.0742°, -39.1192°)", |
| " Mauriti: (-7.3892°, -38.7744°)", |
| " Barreira: (-4.2869°, -38.6431°)", |
| " São Vicente Férrer: (-7.5911°, -35.4914°)", |
| " Maruim: (-10.7375°, -37.0817°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 1698.79 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 153973.70 km²", |
| "FINAL ANSWER: Area: 153973.70 km², Perimeter: 1698.79 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 42.39282, |
| "lon": -83.04964, |
| "name": "Hamtramck" |
| }, |
| { |
| "lat": 45.5608, |
| "lon": -94.16249, |
| "name": "Saint Cloud" |
| }, |
| { |
| "lat": 42.33704, |
| "lon": -71.20922, |
| "name": "Newton" |
| }, |
| { |
| "lat": 39.49983, |
| "lon": -76.64108, |
| "name": "Hunt Valley" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 390459.1, |
| "perimeter_km": 4002.29, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Hamtramck: (42.3928°, -83.0496°)", |
| " Saint Cloud: (45.5608°, -94.1625°)", |
| " Newton: (42.3370°, -71.2092°)", |
| " Hunt Valley: (39.4998°, -76.6411°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4002.29 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 390459.10 km²", |
| "FINAL ANSWER: Area: 390459.10 km², Perimeter: 4002.29 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": -10.06806, |
| "lon": -78.15222, |
| "name": "Huarmey" |
| }, |
| { |
| "lat": -7.73291, |
| "lon": -79.3015, |
| "name": "Paiján" |
| }, |
| { |
| "lat": 0.34881, |
| "lon": -78.12462, |
| "name": "Ibarra" |
| }, |
| { |
| "lat": 5.25397, |
| "lon": -75.15403, |
| "name": "Manzanares" |
| }, |
| { |
| "lat": 5.06692, |
| "lon": -74.59499, |
| "name": "Guaduas" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 321715.71, |
| "perimeter_km": 3627.94, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Huarmey: (-10.0681°, -78.1522°)", |
| " Paiján: (-7.7329°, -79.3015°)", |
| " Ibarra: (0.3488°, -78.1246°)", |
| " Manzanares: (5.2540°, -75.1540°)", |
| " Guaduas: (5.0669°, -74.5950°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3627.94 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 321715.71 km²", |
| "FINAL ANSWER: Area: 321715.71 km², Perimeter: 3627.94 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": -33.93462, |
| "lon": 18.86676, |
| "name": "Stellenbosch" |
| }, |
| { |
| "lat": -33.4608, |
| "lon": 18.72714, |
| "name": "Malmesbury" |
| }, |
| { |
| "lat": -26.26781, |
| "lon": 27.85849, |
| "name": "Soweto" |
| }, |
| { |
| "lat": -29.12107, |
| "lon": 26.214, |
| "name": "Bloemfontein" |
| }, |
| { |
| "lat": -29.19448, |
| "lon": 27.45739, |
| "name": "Ladybrand" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 127421.52, |
| "perimeter_km": 2689.05, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Stellenbosch: (-33.9346°, 18.8668°)", |
| " Malmesbury: (-33.4608°, 18.7271°)", |
| " Soweto: (-26.2678°, 27.8585°)", |
| " Bloemfontein: (-29.1211°, 26.2140°)", |
| " Ladybrand: (-29.1945°, 27.4574°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2689.05 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 127421.52 km²", |
| "FINAL ANSWER: Area: 127421.52 km², Perimeter: 2689.05 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 26.31841, |
| "lon": -80.09977, |
| "name": "Deerfield Beach" |
| }, |
| { |
| "lat": 40.12617, |
| "lon": -82.92907, |
| "name": "Westerville" |
| }, |
| { |
| "lat": 40.60177, |
| "lon": -73.99403, |
| "name": "Bensonhurst" |
| }, |
| { |
| "lat": 41.94454, |
| "lon": -71.28561, |
| "name": "Attleboro" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 722725.94, |
| "perimeter_km": 4502.13, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Deerfield Beach: (26.3184°, -80.0998°)", |
| " Westerville: (40.1262°, -82.9291°)", |
| " Bensonhurst: (40.6018°, -73.9940°)", |
| " Attleboro: (41.9445°, -71.2856°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4502.13 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 722725.94 km²", |
| "FINAL ANSWER: Area: 722725.94 km², Perimeter: 4502.13 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 33.8527, |
| "lon": -7.03171, |
| "name": "Skhirate" |
| }, |
| { |
| "lat": -36.61617, |
| "lon": -64.28991, |
| "name": "Santa Rosa" |
| }, |
| { |
| "lat": 36.09569, |
| "lon": -79.4378, |
| "name": "Burlington" |
| }, |
| { |
| "lat": -6.97038, |
| "lon": 109.64794, |
| "name": "Kedungwuni" |
| }, |
| { |
| "lat": 50.87309, |
| "lon": 4.33419, |
| "name": "Jette" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 105047634.88, |
| "perimeter_km": 48441.43, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Skhirate: (33.8527°, -7.0317°)", |
| " Santa Rosa: (-36.6162°, -64.2899°)", |
| " Burlington: (36.0957°, -79.4378°)", |
| " Kedungwuni: (-6.9704°, 109.6479°)", |
| " Jette: (50.8731°, 4.3342°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 48441.43 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 105047634.88 km²", |
| "FINAL ANSWER: Area: 105047634.88 km², Perimeter: 48441.43 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 32.29876, |
| "lon": -90.18481, |
| "name": "Jackson" |
| }, |
| { |
| "lat": 40.87589, |
| "lon": -81.40234, |
| "name": "North Canton" |
| }, |
| { |
| "lat": 43.85012, |
| "lon": -79.03288, |
| "name": "Ajax" |
| }, |
| { |
| "lat": 39.36415, |
| "lon": -74.42306, |
| "name": "Atlantic City" |
| }, |
| { |
| "lat": 35.26208, |
| "lon": -81.1873, |
| "name": "Gastonia" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 669499.74, |
| "perimeter_km": 3891.75, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Jackson: (32.2988°, -90.1848°)", |
| " North Canton: (40.8759°, -81.4023°)", |
| " Ajax: (43.8501°, -79.0329°)", |
| " Atlantic City: (39.3642°, -74.4231°)", |
| " Gastonia: (35.2621°, -81.1873°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3891.75 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 669499.74 km²", |
| "FINAL ANSWER: Area: 669499.74 km², Perimeter: 3891.75 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": 37.72727, |
| "lon": -89.21675, |
| "name": "Carbondale" |
| }, |
| { |
| "lat": 45.3001, |
| "lon": -75.91606, |
| "name": "Kanata" |
| }, |
| { |
| "lat": 45.5152, |
| "lon": -73.46818, |
| "name": "Longueuil" |
| }, |
| { |
| "lat": 42.3501, |
| "lon": -71.15644, |
| "name": "Brighton" |
| }, |
| { |
| "lat": 40.8126, |
| "lon": -73.88402, |
| "name": "Hunts Point" |
| }, |
| { |
| "lat": 39.32928, |
| "lon": -76.54463, |
| "name": "Frankford" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 543716.69, |
| "perimeter_km": 3658.18, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Carbondale: (37.7273°, -89.2168°)", |
| " Kanata: (45.3001°, -75.9161°)", |
| " Longueuil: (45.5152°, -73.4682°)", |
| " Brighton: (42.3501°, -71.1564°)", |
| " Hunts Point: (40.8126°, -73.8840°)", |
| " Frankford: (39.3293°, -76.5446°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3658.18 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 543716.69 km²", |
| "FINAL ANSWER: Area: 543716.69 km², Perimeter: 3658.18 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": -37.82289, |
| "lon": 147.61041, |
| "name": "Bairnsdale" |
| }, |
| { |
| "lat": -37.83382, |
| "lon": 144.93834, |
| "name": "City of Port Phillip" |
| }, |
| { |
| "lat": -38.14711, |
| "lon": 144.36069, |
| "name": "Geelong" |
| }, |
| { |
| "lat": -27.56056, |
| "lon": 151.95386, |
| "name": "Toowoomba" |
| }, |
| { |
| "lat": -33.52314, |
| "lon": 151.31325, |
| "name": "Umina Beach" |
| }, |
| { |
| "lat": -33.95, |
| "lon": 151.13333, |
| "name": "Rockdale" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 253381.39, |
| "perimeter_km": 2920.2, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Bairnsdale: (-37.8229°, 147.6104°)", |
| " City of Port Phillip: (-37.8338°, 144.9383°)", |
| " Geelong: (-38.1471°, 144.3607°)", |
| " Toowoomba: (-27.5606°, 151.9539°)", |
| " Umina Beach: (-33.5231°, 151.3133°)", |
| " Rockdale: (-33.9500°, 151.1333°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2920.20 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 253381.39 km²", |
| "FINAL ANSWER: Area: 253381.39 km², Perimeter: 2920.20 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": -34.78254, |
| "lon": 138.61077, |
| "name": "Parafield Gardens" |
| }, |
| { |
| "lat": -19.26639, |
| "lon": 146.80569, |
| "name": "Townsville" |
| }, |
| { |
| "lat": -27.63917, |
| "lon": 153.10944, |
| "name": "Logan City" |
| }, |
| { |
| "lat": -33.79798, |
| "lon": 151.28826, |
| "name": "Manly" |
| }, |
| { |
| "lat": -34.4279, |
| "lon": 150.89268, |
| "name": "Wollongong city centre" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1322031.56, |
| "perimeter_km": 4945.32, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Parafield Gardens: (-34.7825°, 138.6108°)", |
| " Townsville: (-19.2664°, 146.8057°)", |
| " Logan City: (-27.6392°, 153.1094°)", |
| " Manly: (-33.7980°, 151.2883°)", |
| " Wollongong city centre: (-34.4279°, 150.8927°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4945.32 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1322031.56 km²", |
| "FINAL ANSWER: Area: 1322031.56 km², Perimeter: 4945.32 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 1.3651, |
| "lon": 104.1118, |
| "name": "Pengerang" |
| }, |
| { |
| "lat": 2.2635, |
| "lon": 102.2179, |
| "name": "Kampung Cheng" |
| }, |
| { |
| "lat": 16.63557, |
| "lon": 97.61526, |
| "name": "Hmaw Bi" |
| }, |
| { |
| "lat": -0.49167, |
| "lon": 117.14583, |
| "name": "Samarinda" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1330525.31, |
| "perimeter_km": 6238.13, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Pengerang: (1.3651°, 104.1118°)", |
| " Kampung Cheng: (2.2635°, 102.2179°)", |
| " Hmaw Bi: (16.6356°, 97.6153°)", |
| " Samarinda: (-0.4917°, 117.1458°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 6238.13 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1330525.31 km²", |
| "FINAL ANSWER: Area: 1330525.31 km², Perimeter: 6238.13 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 30.17173, |
| "lon": 107.22991, |
| "name": "Haitang" |
| }, |
| { |
| "lat": 34.73564, |
| "lon": 105.32632, |
| "name": "Gangu Chengguanzhen" |
| }, |
| { |
| "lat": 36.95389, |
| "lon": 118.10472, |
| "name": "Suozhen" |
| }, |
| { |
| "lat": 20.03421, |
| "lon": 110.34651, |
| "name": "Haikou" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 997750.09, |
| "perimeter_km": 4911.21, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Haitang: (30.1717°, 107.2299°)", |
| " Gangu Chengguanzhen: (34.7356°, 105.3263°)", |
| " Suozhen: (36.9539°, 118.1047°)", |
| " Haikou: (20.0342°, 110.3465°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4911.21 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 997750.09 km²", |
| "FINAL ANSWER: Area: 997750.09 km², Perimeter: 4911.21 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 5.20913, |
| "lon": -1.06058, |
| "name": "Saltpond" |
| }, |
| { |
| "lat": 7.92807, |
| "lon": 1.97558, |
| "name": "Savalou" |
| }, |
| { |
| "lat": 10.49222, |
| "lon": 0.99972, |
| "name": "Cobly" |
| }, |
| { |
| "lat": 5.1009, |
| "lon": 6.81411, |
| "name": "Elele" |
| }, |
| { |
| "lat": 6.41502, |
| "lon": 2.88132, |
| "name": "Badagry" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 382074.67, |
| "perimeter_km": 2548.41, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Saltpond: (5.2091°, -1.0606°)", |
| " Savalou: (7.9281°, 1.9756°)", |
| " Cobly: (10.4922°, 0.9997°)", |
| " Elele: (5.1009°, 6.8141°)", |
| " Badagry: (6.4150°, 2.8813°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2548.41 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 382074.67 km²", |
| "FINAL ANSWER: Area: 382074.67 km², Perimeter: 2548.41 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 47.17941, |
| "lon": -1.62468, |
| "name": "Bouguenais" |
| }, |
| { |
| "lat": 49.62612, |
| "lon": -1.64349, |
| "name": "Octeville" |
| }, |
| { |
| "lat": 51.43092, |
| "lon": -0.50606, |
| "name": "Staines" |
| }, |
| { |
| "lat": 48.75329, |
| "lon": 2.29668, |
| "name": "Antony" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 71818.86, |
| "perimeter_km": 1187.16, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Bouguenais: (47.1794°, -1.6247°)", |
| " Octeville: (49.6261°, -1.6435°)", |
| " Staines: (51.4309°, -0.5061°)", |
| " Antony: (48.7533°, 2.2967°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 1187.16 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 71818.86 km²", |
| "FINAL ANSWER: Area: 71818.86 km², Perimeter: 1187.16 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": 38.01539, |
| "lon": 23.69187, |
| "name": "Peristéri" |
| }, |
| { |
| "lat": 45.59665, |
| "lon": 9.88688, |
| "name": "Palazzolo sull'Oglio" |
| }, |
| { |
| "lat": 52.67631, |
| "lon": 13.27775, |
| "name": "Hohen Neuendorf" |
| }, |
| { |
| "lat": 58.59382, |
| "lon": 35.80244, |
| "name": "Pestovo" |
| }, |
| { |
| "lat": 55.86667, |
| "lon": 37.58333, |
| "name": "Slobodka" |
| }, |
| { |
| "lat": 48.50834, |
| "lon": 32.26618, |
| "name": "Kropyvnytskyy" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 2406360.85, |
| "perimeter_km": 6363.82, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Peristéri: (38.0154°, 23.6919°)", |
| " Palazzolo sull'Oglio: (45.5966°, 9.8869°)", |
| " Hohen Neuendorf: (52.6763°, 13.2777°)", |
| " Pestovo: (58.5938°, 35.8024°)", |
| " Slobodka: (55.8667°, 37.5833°)", |
| " Kropyvnytskyy: (48.5083°, 32.2662°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 6363.82 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 2406360.85 km²", |
| "FINAL ANSWER: Area: 2406360.85 km², Perimeter: 6363.82 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 6.1162, |
| "lon": -6.53603, |
| "name": "Grand-Zattry" |
| }, |
| { |
| "lat": 14.00776, |
| "lon": 0.75306, |
| "name": "Téra" |
| }, |
| { |
| "lat": 5.71417, |
| "lon": -0.15418, |
| "name": "Adenta" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 328743.22, |
| "perimeter_km": 2820.44, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Grand-Zattry: (6.1162°, -6.5360°)", |
| " Téra: (14.0078°, 0.7531°)", |
| " Adenta: (5.7142°, -0.1542°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2820.44 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 328743.22 km²", |
| "FINAL ANSWER: Area: 328743.22 km², Perimeter: 2820.44 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": -21.18972, |
| "lon": -46.98028, |
| "name": "Monte Santo de Minas" |
| }, |
| { |
| "lat": -17.31472, |
| "lon": -53.21528, |
| "name": "Alto Araguaia" |
| }, |
| { |
| "lat": -15.76194, |
| "lon": -48.28167, |
| "name": "Águas Lindas de Goiás" |
| }, |
| { |
| "lat": -6.24444, |
| "lon": -38.91361, |
| "name": "Orós" |
| }, |
| { |
| "lat": -11.13556, |
| "lon": -42.11278, |
| "name": "Central" |
| }, |
| { |
| "lat": -18.37333, |
| "lon": -40.83056, |
| "name": "Ecoporanga" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 900117.01, |
| "perimeter_km": 4987.19, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Monte Santo de Minas: (-21.1897°, -46.9803°)", |
| " Alto Araguaia: (-17.3147°, -53.2153°)", |
| " Águas Lindas de Goiás: (-15.7619°, -48.2817°)", |
| " Orós: (-6.2444°, -38.9136°)", |
| " Central: (-11.1356°, -42.1128°)", |
| " Ecoporanga: (-18.3733°, -40.8306°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4987.19 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 900117.01 km²", |
| "FINAL ANSWER: Area: 900117.01 km², Perimeter: 4987.19 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 40.06396, |
| "lon": -80.72091, |
| "name": "Wheeling" |
| }, |
| { |
| "lat": 39.43534, |
| "lon": -84.20299, |
| "name": "Lebanon" |
| }, |
| { |
| "lat": 43.73766, |
| "lon": -79.34972, |
| "name": "Banbury-Don Mills" |
| }, |
| { |
| "lat": 42.52509, |
| "lon": -71.75979, |
| "name": "Leominster" |
| }, |
| { |
| "lat": 36.71709, |
| "lon": -76.59023, |
| "name": "South Suffolk" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 381570.07, |
| "perimeter_km": 2846.03, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Wheeling: (40.0640°, -80.7209°)", |
| " Lebanon: (39.4353°, -84.2030°)", |
| " Banbury-Don Mills: (43.7377°, -79.3497°)", |
| " Leominster: (42.5251°, -71.7598°)", |
| " South Suffolk: (36.7171°, -76.5902°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2846.03 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 381570.07 km²", |
| "FINAL ANSWER: Area: 381570.07 km², Perimeter: 2846.03 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 36.13968, |
| "lon": -120.36015, |
| "name": "Coalinga" |
| }, |
| { |
| "lat": 35.14778, |
| "lon": -114.5683, |
| "name": "Bullhead City" |
| }, |
| { |
| "lat": 33.24866, |
| "lon": -111.6343, |
| "name": "Queen Creek" |
| }, |
| { |
| "lat": 34.23087, |
| "lon": -111.32514, |
| "name": "Payson" |
| }, |
| { |
| "lat": 20.23031, |
| "lon": -99.21396, |
| "name": "Mixquiahuala de Juarez" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 537972.1, |
| "perimeter_km": 5664.12, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Coalinga: (36.1397°, -120.3602°)", |
| " Bullhead City: (35.1478°, -114.5683°)", |
| " Queen Creek: (33.2487°, -111.6343°)", |
| " Payson: (34.2309°, -111.3251°)", |
| " Mixquiahuala de Juarez: (20.2303°, -99.2140°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5664.12 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 537972.10 km²", |
| "FINAL ANSWER: Area: 537972.10 km², Perimeter: 5664.12 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 31.28244, |
| "lon": -4.26541, |
| "name": "Moulay Ali Cherif" |
| }, |
| { |
| "lat": 35.23464, |
| "lon": -0.24435, |
| "name": "Sfizef" |
| }, |
| { |
| "lat": 36.66774, |
| "lon": 3.59115, |
| "name": "Beni Amrane" |
| }, |
| { |
| "lat": 36.33293, |
| "lon": 5.08843, |
| "name": "Bougaa" |
| }, |
| { |
| "lat": 27.05, |
| "lon": 14.4, |
| "name": "Al Jadīd" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 780380.15, |
| "perimeter_km": 4321.37, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Moulay Ali Cherif: (31.2824°, -4.2654°)", |
| " Sfizef: (35.2346°, -0.2444°)", |
| " Beni Amrane: (36.6677°, 3.5911°)", |
| " Bougaa: (36.3329°, 5.0884°)", |
| " Al Jadīd: (27.0500°, 14.4000°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4321.37 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 780380.15 km²", |
| "FINAL ANSWER: Area: 780380.15 km², Perimeter: 4321.37 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 19.68006, |
| "lon": -103.2514, |
| "name": "Tamazula de Gordiano" |
| }, |
| { |
| "lat": 33.44179, |
| "lon": -94.03769, |
| "name": "Texarkana" |
| }, |
| { |
| "lat": 25.90175, |
| "lon": -97.49748, |
| "name": "Brownsville" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 146181.76, |
| "perimeter_km": 3592.8, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Tamazula de Gordiano: (19.6801°, -103.2514°)", |
| " Texarkana: (33.4418°, -94.0377°)", |
| " Brownsville: (25.9017°, -97.4975°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3592.80 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 146181.76 km²", |
| "FINAL ANSWER: Area: 146181.76 km², Perimeter: 3592.80 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": -41.51603, |
| "lon": 173.9528, |
| "name": "Blenheim" |
| }, |
| { |
| "lat": -35.73167, |
| "lon": 174.32391, |
| "name": "Whangarei" |
| }, |
| { |
| "lat": -36.93754, |
| "lon": 174.65584, |
| "name": "Titirangi" |
| }, |
| { |
| "lat": -39.4926, |
| "lon": 176.91233, |
| "name": "Napier" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 69280.78, |
| "perimeter_km": 1463.58, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Blenheim: (-41.5160°, 173.9528°)", |
| " Whangarei: (-35.7317°, 174.3239°)", |
| " Titirangi: (-36.9375°, 174.6558°)", |
| " Napier: (-39.4926°, 176.9123°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 1463.58 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 69280.78 km²", |
| "FINAL ANSWER: Area: 69280.78 km², Perimeter: 1463.58 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 49.27784, |
| "lon": -123.12794, |
| "name": "Downtown" |
| }, |
| { |
| "lat": 37.05828, |
| "lon": -120.84992, |
| "name": "Los Banos" |
| }, |
| { |
| "lat": 37.6391, |
| "lon": -120.99688, |
| "name": "Modesto" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 3439.7, |
| "perimeter_km": 2742.36, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Downtown: (49.2778°, -123.1279°)", |
| " Los Banos: (37.0583°, -120.8499°)", |
| " Modesto: (37.6391°, -120.9969°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2742.36 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 3439.70 km²", |
| "FINAL ANSWER: Area: 3439.70 km², Perimeter: 2742.36 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 48.98333, |
| "lon": 2.23333, |
| "name": "Franconville" |
| }, |
| { |
| "lat": 53.47497, |
| "lon": -2.08809, |
| "name": "Dukinfield" |
| }, |
| { |
| "lat": 51.38333, |
| "lon": 8.08333, |
| "name": "Arnsberg" |
| }, |
| { |
| "lat": 50.32174, |
| "lon": 10.20673, |
| "name": "Bad Neustadt an der Saale" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 187181.51, |
| "perimeter_km": 2092.66, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Franconville: (48.9833°, 2.2333°)", |
| " Dukinfield: (53.4750°, -2.0881°)", |
| " Arnsberg: (51.3833°, 8.0833°)", |
| " Bad Neustadt an der Saale: (50.3217°, 10.2067°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2092.66 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 187181.51 km²", |
| "FINAL ANSWER: Area: 187181.51 km², Perimeter: 2092.66 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 43.58508, |
| "lon": 5.00268, |
| "name": "Miramas" |
| }, |
| { |
| "lat": 54.53478, |
| "lon": -1.05606, |
| "name": "Guisborough" |
| }, |
| { |
| "lat": 54.03374, |
| "lon": 22.50704, |
| "name": "Olecko" |
| }, |
| { |
| "lat": 49.86899, |
| "lon": 8.9321, |
| "name": "Groß-Umstadt" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1177958.0, |
| "perimeter_km": 4614.17, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Miramas: (43.5851°, 5.0027°)", |
| " Guisborough: (54.5348°, -1.0561°)", |
| " Olecko: (54.0337°, 22.5070°)", |
| " Groß-Umstadt: (49.8690°, 8.9321°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4614.17 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1177958.00 km²", |
| "FINAL ANSWER: Area: 1177958.00 km², Perimeter: 4614.17 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": -1.89969, |
| "lon": -50.20821, |
| "name": "Bagre" |
| }, |
| { |
| "lat": -22.4325, |
| "lon": -46.5725, |
| "name": "Monte Sião" |
| }, |
| { |
| "lat": -17.29972, |
| "lon": -48.27944, |
| "name": "Pires do Rio" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 89512.49, |
| "perimeter_km": 4639.99, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Bagre: (-1.8997°, -50.2082°)", |
| " Monte Sião: (-22.4325°, -46.5725°)", |
| " Pires do Rio: (-17.2997°, -48.2794°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4639.99 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 89512.49 km²", |
| "FINAL ANSWER: Area: 89512.49 km², Perimeter: 4639.99 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 33.9526, |
| "lon": -84.54993, |
| "name": "Marietta" |
| }, |
| { |
| "lat": 42.1103, |
| "lon": -88.03424, |
| "name": "Palatine" |
| }, |
| { |
| "lat": 44.88969, |
| "lon": -93.34995, |
| "name": "Edina" |
| }, |
| { |
| "lat": 41.39482, |
| "lon": -73.45401, |
| "name": "Danbury" |
| }, |
| { |
| "lat": 40.84288, |
| "lon": -73.29289, |
| "name": "Commack" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1063190.04, |
| "perimeter_km": 4457.33, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Marietta: (33.9526°, -84.5499°)", |
| " Palatine: (42.1103°, -88.0342°)", |
| " Edina: (44.8897°, -93.3500°)", |
| " Danbury: (41.3948°, -73.4540°)", |
| " Commack: (40.8429°, -73.2929°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4457.33 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1063190.04 km²", |
| "FINAL ANSWER: Area: 1063190.04 km², Perimeter: 4457.33 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": -37.88264, |
| "lon": 144.7003, |
| "name": "Hoppers Crossing" |
| }, |
| { |
| "lat": -36.35846, |
| "lon": 146.32056, |
| "name": "Wangaratta" |
| }, |
| { |
| "lat": -33.78333, |
| "lon": 150.93333, |
| "name": "Seven Hills" |
| }, |
| { |
| "lat": -35.41647, |
| "lon": 149.06954, |
| "name": "Tuggeranong Administrative District" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 26910.48, |
| "perimeter_km": 1455.85, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Hoppers Crossing: (-37.8826°, 144.7003°)", |
| " Wangaratta: (-36.3585°, 146.3206°)", |
| " Seven Hills: (-33.7833°, 150.9333°)", |
| " Tuggeranong Administrative District: (-35.4165°, 149.0695°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 1455.85 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 26910.48 km²", |
| "FINAL ANSWER: Area: 26910.48 km², Perimeter: 1455.85 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": -44.39672, |
| "lon": 171.25364, |
| "name": "Timaru" |
| }, |
| { |
| "lat": -36.8582, |
| "lon": 174.62019, |
| "name": "Lincoln" |
| }, |
| { |
| "lat": -37.78821, |
| "lon": 175.2902, |
| "name": "Hamilton East" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 38765.86, |
| "perimeter_km": 1812.73, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Timaru: (-44.3967°, 171.2536°)", |
| " Lincoln: (-36.8582°, 174.6202°)", |
| " Hamilton East: (-37.7882°, 175.2902°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 1812.73 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 38765.86 km²", |
| "FINAL ANSWER: Area: 38765.86 km², Perimeter: 1812.73 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": -34.75705, |
| "lon": 138.60819, |
| "name": "Paralowie" |
| }, |
| { |
| "lat": -33.28397, |
| "lon": 149.10018, |
| "name": "Orange" |
| }, |
| { |
| "lat": -37.81501, |
| "lon": 144.96657, |
| "name": "Melbourne City Centre" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 206000.92, |
| "perimeter_km": 2270.95, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Paralowie: (-34.7570°, 138.6082°)", |
| " Orange: (-33.2840°, 149.1002°)", |
| " Melbourne City Centre: (-37.8150°, 144.9666°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2270.95 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 206000.92 km²", |
| "FINAL ANSWER: Area: 206000.92 km², Perimeter: 2270.95 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 34.34381, |
| "lon": 3.22475, |
| "name": "’Aïn el Bell" |
| }, |
| { |
| "lat": 35.93115, |
| "lon": 0.08918, |
| "name": "Mostaganem" |
| }, |
| { |
| "lat": 36.67446, |
| "lon": 10.15633, |
| "name": "La Mohammedia" |
| }, |
| { |
| "lat": 35.82539, |
| "lon": 10.63699, |
| "name": "Sousse" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 130847.39, |
| "perimeter_km": 2038.67, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " ’Aïn el Bell: (34.3438°, 3.2247°)", |
| " Mostaganem: (35.9312°, 0.0892°)", |
| " La Mohammedia: (36.6745°, 10.1563°)", |
| " Sousse: (35.8254°, 10.6370°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2038.67 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 130847.39 km²", |
| "FINAL ANSWER: Area: 130847.39 km², Perimeter: 2038.67 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": -42.76848, |
| "lon": -65.03827, |
| "name": "Puerto Madryn" |
| }, |
| { |
| "lat": -32.83369, |
| "lon": -70.59827, |
| "name": "Los Andes" |
| }, |
| { |
| "lat": -32.17675, |
| "lon": -64.11295, |
| "name": "Río Tercero" |
| }, |
| { |
| "lat": -27.80047, |
| "lon": -64.26285, |
| "name": "Santiago del Estero" |
| }, |
| { |
| "lat": -29.37639, |
| "lon": -51.11444, |
| "name": "Nova Petrópolis" |
| }, |
| { |
| "lat": -29.91778, |
| "lon": -51.18361, |
| "name": "Canoas" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1484740.75, |
| "perimeter_km": 5549.31, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Puerto Madryn: (-42.7685°, -65.0383°)", |
| " Los Andes: (-32.8337°, -70.5983°)", |
| " Río Tercero: (-32.1767°, -64.1129°)", |
| " Santiago del Estero: (-27.8005°, -64.2629°)", |
| " Nova Petrópolis: (-29.3764°, -51.1144°)", |
| " Canoas: (-29.9178°, -51.1836°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5549.31 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1484740.75 km²", |
| "FINAL ANSWER: Area: 1484740.75 km², Perimeter: 5549.31 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": 37.89013, |
| "lon": 23.74406, |
| "name": "Ellinikó" |
| }, |
| { |
| "lat": 59.51839, |
| "lon": 17.91128, |
| "name": "Upplands Väsby" |
| }, |
| { |
| "lat": 63.11418, |
| "lon": 21.68216, |
| "name": "Korsholm" |
| }, |
| { |
| "lat": 52.04479, |
| "lon": 39.72569, |
| "name": "Usman’" |
| }, |
| { |
| "lat": 48.2824, |
| "lon": 37.17772, |
| "name": "Pokrovsk" |
| }, |
| { |
| "lat": 44.0834, |
| "lon": 41.9763, |
| "name": "Ust’-Dzheguta" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 2592535.81, |
| "perimeter_km": 7235.7, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Ellinikó: (37.8901°, 23.7441°)", |
| " Upplands Väsby: (59.5184°, 17.9113°)", |
| " Korsholm: (63.1142°, 21.6822°)", |
| " Usman’: (52.0448°, 39.7257°)", |
| " Pokrovsk: (48.2824°, 37.1777°)", |
| " Ust’-Dzheguta: (44.0834°, 41.9763°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 7235.70 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 2592535.81 km²", |
| "FINAL ANSWER: Area: 2592535.81 km², Perimeter: 7235.70 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": -30.72644, |
| "lon": -64.80387, |
| "name": "Cruz del Eje" |
| }, |
| { |
| "lat": -18.54389, |
| "lon": -53.12917, |
| "name": "Costa Rica" |
| }, |
| { |
| "lat": -20.08667, |
| "lon": -51.09361, |
| "name": "Aparecida do Taboado" |
| }, |
| { |
| "lat": -21.22583, |
| "lon": -43.77361, |
| "name": "Barbacena" |
| }, |
| { |
| "lat": -23.55242, |
| "lon": -46.65735, |
| "name": "Consolação" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 907518.54, |
| "perimeter_km": 5194.8, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Cruz del Eje: (-30.7264°, -64.8039°)", |
| " Costa Rica: (-18.5439°, -53.1292°)", |
| " Aparecida do Taboado: (-20.0867°, -51.0936°)", |
| " Barbacena: (-21.2258°, -43.7736°)", |
| " Consolação: (-23.5524°, -46.6574°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5194.80 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 907518.54 km²", |
| "FINAL ANSWER: Area: 907518.54 km², Perimeter: 5194.80 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": -13.686, |
| "lon": -39.47803, |
| "name": "Wenceslau Guimarães" |
| }, |
| { |
| "lat": -9.91722, |
| "lon": -37.27833, |
| "name": "Porto da Folha" |
| }, |
| { |
| "lat": -7.50528, |
| "lon": -35.31833, |
| "name": "Timbaúba" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 13586.04, |
| "perimeter_km": 1650.51, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Wenceslau Guimarães: (-13.6860°, -39.4780°)", |
| " Porto da Folha: (-9.9172°, -37.2783°)", |
| " Timbaúba: (-7.5053°, -35.3183°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 1650.51 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 13586.04 km²", |
| "FINAL ANSWER: Area: 13586.04 km², Perimeter: 1650.51 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 47.49702, |
| "lon": 7.59172, |
| "name": "Reinach" |
| }, |
| { |
| "lat": 51.86568, |
| "lon": -2.2431, |
| "name": "Gloucester" |
| }, |
| { |
| "lat": 53.4273, |
| "lon": 14.51303, |
| "name": "Świerczewo" |
| }, |
| { |
| "lat": 45.88333, |
| "lon": 22.9, |
| "name": "Deva" |
| }, |
| { |
| "lat": 40.57762, |
| "lon": 17.03812, |
| "name": "Palagiano" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1167177.45, |
| "perimeter_km": 4863.6, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Reinach: (47.4970°, 7.5917°)", |
| " Gloucester: (51.8657°, -2.2431°)", |
| " Świerczewo: (53.4273°, 14.5130°)", |
| " Deva: (45.8833°, 22.9000°)", |
| " Palagiano: (40.5776°, 17.0381°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4863.60 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1167177.45 km²", |
| "FINAL ANSWER: Area: 1167177.45 km², Perimeter: 4863.60 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": -23.5275, |
| "lon": -46.9025, |
| "name": "Jandira" |
| }, |
| { |
| "lat": -26.07361, |
| "lon": -53.72528, |
| "name": "Santo Antônio do Sudoeste" |
| }, |
| { |
| "lat": -14.06944, |
| "lon": -42.475, |
| "name": "Caetité" |
| }, |
| { |
| "lat": -8.07361, |
| "lon": -37.26444, |
| "name": "Sertânia" |
| }, |
| { |
| "lat": -20.12389, |
| "lon": -42.00139, |
| "name": "Simonésia" |
| }, |
| { |
| "lat": -19.81, |
| "lon": -43.17361, |
| "name": "João Monlevade" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 708336.64, |
| "perimeter_km": 5522.69, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Jandira: (-23.5275°, -46.9025°)", |
| " Santo Antônio do Sudoeste: (-26.0736°, -53.7253°)", |
| " Caetité: (-14.0694°, -42.4750°)", |
| " Sertânia: (-8.0736°, -37.2644°)", |
| " Simonésia: (-20.1239°, -42.0014°)", |
| " João Monlevade: (-19.8100°, -43.1736°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5522.69 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 708336.64 km²", |
| "FINAL ANSWER: Area: 708336.64 km², Perimeter: 5522.69 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": -2.63199, |
| "lon": -80.38808, |
| "name": "Playas" |
| }, |
| { |
| "lat": 5.69188, |
| "lon": -76.65835, |
| "name": "Quibdó" |
| }, |
| { |
| "lat": 5.13278, |
| "lon": -74.15977, |
| "name": "Pacho" |
| }, |
| { |
| "lat": 7.81348, |
| "lon": -71.17788, |
| "name": "Santa Bárbara" |
| }, |
| { |
| "lat": -12.08628, |
| "lon": -75.20827, |
| "name": "Chilca" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1056058.41, |
| "perimeter_km": 5195.07, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Playas: (-2.6320°, -80.3881°)", |
| " Quibdó: (5.6919°, -76.6583°)", |
| " Pacho: (5.1328°, -74.1598°)", |
| " Santa Bárbara: (7.8135°, -71.1779°)", |
| " Chilca: (-12.0863°, -75.2083°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5195.07 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1056058.41 km²", |
| "FINAL ANSWER: Area: 1056058.41 km², Perimeter: 5195.07 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": -23.59468, |
| "lon": -46.54359, |
| "name": "Sao Lucas" |
| }, |
| { |
| "lat": -22.7775, |
| "lon": -47.29583, |
| "name": "Nova Odessa" |
| }, |
| { |
| "lat": -6.60167, |
| "lon": -44.07667, |
| "name": "Pastos Bons" |
| }, |
| { |
| "lat": -11.00861, |
| "lon": -44.51944, |
| "name": "Santa Rita de Cássia" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 102705.46, |
| "perimeter_km": 3858.72, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Sao Lucas: (-23.5947°, -46.5436°)", |
| " Nova Odessa: (-22.7775°, -47.2958°)", |
| " Pastos Bons: (-6.6017°, -44.0767°)", |
| " Santa Rita de Cássia: (-11.0086°, -44.5194°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3858.72 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 102705.46 km²", |
| "FINAL ANSWER: Area: 102705.46 km², Perimeter: 3858.72 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 41.85059, |
| "lon": -87.79367, |
| "name": "Berwyn" |
| }, |
| { |
| "lat": 43.76489, |
| "lon": -79.52198, |
| "name": "Black Creek" |
| }, |
| { |
| "lat": 44.77599, |
| "lon": -63.67865, |
| "name": "Lower Sackville" |
| }, |
| { |
| "lat": 40.73232, |
| "lon": -74.23487, |
| "name": "Irvington" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 403878.76, |
| "perimeter_km": 4081.1, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Berwyn: (41.8506°, -87.7937°)", |
| " Black Creek: (43.7649°, -79.5220°)", |
| " Lower Sackville: (44.7760°, -63.6786°)", |
| " Irvington: (40.7323°, -74.2349°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4081.10 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 403878.76 km²", |
| "FINAL ANSWER: Area: 403878.76 km², Perimeter: 4081.10 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": -41.05584, |
| "lon": 145.90375, |
| "name": "Burnie" |
| }, |
| { |
| "lat": -37.87397, |
| "lon": 145.04253, |
| "name": "Malvern East" |
| }, |
| { |
| "lat": -20.72523, |
| "lon": 139.49727, |
| "name": "Mount Isa" |
| }, |
| { |
| "lat": -27.19354, |
| "lon": 153.02631, |
| "name": "Deception Bay" |
| }, |
| { |
| "lat": -30.29626, |
| "lon": 153.11351, |
| "name": "Coffs Harbour" |
| }, |
| { |
| "lat": -33.78269, |
| "lon": 151.04888, |
| "name": "Carlingford" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1458150.81, |
| "perimeter_km": 5597.66, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Burnie: (-41.0558°, 145.9038°)", |
| " Malvern East: (-37.8740°, 145.0425°)", |
| " Mount Isa: (-20.7252°, 139.4973°)", |
| " Deception Bay: (-27.1935°, 153.0263°)", |
| " Coffs Harbour: (-30.2963°, 153.1135°)", |
| " Carlingford: (-33.7827°, 151.0489°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5597.66 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1458150.81 km²", |
| "FINAL ANSWER: Area: 1458150.81 km², Perimeter: 5597.66 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 10.05154, |
| "lon": -75.26775, |
| "name": "San Pablo" |
| }, |
| { |
| "lat": 10.96854, |
| "lon": -74.78132, |
| "name": "Barranquilla" |
| }, |
| { |
| "lat": 8.39925, |
| "lon": -71.64082, |
| "name": "Santa Cruz de Mora" |
| }, |
| { |
| "lat": -7.05056, |
| "lon": -71.69472, |
| "name": "Ipixuna" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 369782.57, |
| "perimeter_km": 4222.67, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " San Pablo: (10.0515°, -75.2678°)", |
| " Barranquilla: (10.9685°, -74.7813°)", |
| " Santa Cruz de Mora: (8.3993°, -71.6408°)", |
| " Ipixuna: (-7.0506°, -71.6947°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4222.67 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 369782.57 km²", |
| "FINAL ANSWER: Area: 369782.57 km², Perimeter: 4222.67 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 40.66772, |
| "lon": -111.93883, |
| "name": "Taylorsville" |
| }, |
| { |
| "lat": 38.20007, |
| "lon": -85.82274, |
| "name": "Shively" |
| }, |
| { |
| "lat": 33.16262, |
| "lon": -96.93751, |
| "name": "Little Elm" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 850009.27, |
| "perimeter_km": 4969.54, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Taylorsville: (40.6677°, -111.9388°)", |
| " Shively: (38.2001°, -85.8227°)", |
| " Little Elm: (33.1626°, -96.9375°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4969.54 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 850009.27 km²", |
| "FINAL ANSWER: Area: 850009.27 km², Perimeter: 4969.54 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": -7.3, |
| "lon": 20.73333, |
| "name": "Chitato" |
| }, |
| { |
| "lat": -3.28333, |
| "lon": 31.52583, |
| "name": "Uyovu" |
| }, |
| { |
| "lat": -3.49194, |
| "lon": 31.96389, |
| "name": "Ushirombo" |
| }, |
| { |
| "lat": -6.08125, |
| "lon": 36.64657, |
| "name": "Kibaigwa" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 318889.73, |
| "perimeter_km": 3685.21, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Chitato: (-7.3000°, 20.7333°)", |
| " Uyovu: (-3.2833°, 31.5258°)", |
| " Ushirombo: (-3.4919°, 31.9639°)", |
| " Kibaigwa: (-6.0812°, 36.6466°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3685.21 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 318889.73 km²", |
| "FINAL ANSWER: Area: 318889.73 km², Perimeter: 3685.21 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": 13.95114, |
| "lon": 101.71769, |
| "name": "Kabin Buri" |
| }, |
| { |
| "lat": 29.32431, |
| "lon": 107.76056, |
| "name": "Wulong" |
| }, |
| { |
| "lat": 39.1375, |
| "lon": 116.99972, |
| "name": "Yangliuqing" |
| }, |
| { |
| "lat": 39.76538, |
| "lon": 118.41191, |
| "name": "Zhaogezhuang" |
| }, |
| { |
| "lat": 13.902, |
| "lon": 121.0521, |
| "name": "Cuenca" |
| }, |
| { |
| "lat": 22.28399, |
| "lon": 114.14958, |
| "name": "Mid Levels" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 4424513.23, |
| "perimeter_km": 9016.72, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Kabin Buri: (13.9511°, 101.7177°)", |
| " Wulong: (29.3243°, 107.7606°)", |
| " Yangliuqing: (39.1375°, 116.9997°)", |
| " Zhaogezhuang: (39.7654°, 118.4119°)", |
| " Cuenca: (13.9020°, 121.0521°)", |
| " Mid Levels: (22.2840°, 114.1496°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 9016.72 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 4424513.23 km²", |
| "FINAL ANSWER: Area: 4424513.23 km², Perimeter: 9016.72 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": 5.09053, |
| "lon": -6.34438, |
| "name": "Lobakuya" |
| }, |
| { |
| "lat": 5.61411, |
| "lon": -1.5502, |
| "name": "Twifu Praso" |
| }, |
| { |
| "lat": 6.42611, |
| "lon": 1.21333, |
| "name": "Tsévié" |
| }, |
| { |
| "lat": 3.51667, |
| "lon": 11.5, |
| "name": "Mbalmayo" |
| }, |
| { |
| "lat": 0.00694, |
| "lon": 15.63333, |
| "name": "Makoua" |
| }, |
| { |
| "lat": -7.35207, |
| "lon": 14.84629, |
| "name": "Songo" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1614370.22, |
| "perimeter_km": 6190.72, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Lobakuya: (5.0905°, -6.3444°)", |
| " Twifu Praso: (5.6141°, -1.5502°)", |
| " Tsévié: (6.4261°, 1.2133°)", |
| " Mbalmayo: (3.5167°, 11.5000°)", |
| " Makoua: (0.0069°, 15.6333°)", |
| " Songo: (-7.3521°, 14.8463°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 6190.72 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1614370.22 km²", |
| "FINAL ANSWER: Area: 1614370.22 km², Perimeter: 6190.72 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 29.14816, |
| "lon": 31.12733, |
| "name": "Būsh" |
| }, |
| { |
| "lat": 31.16844, |
| "lon": 31.7655, |
| "name": "Kafr al Kurdī" |
| }, |
| { |
| "lat": 30.31263, |
| "lon": 32.30935, |
| "name": "Fāyīd" |
| }, |
| { |
| "lat": 14.0012, |
| "lon": 32.3116, |
| "name": "Ad Douiem" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 113490.19, |
| "perimeter_km": 3843.72, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Būsh: (29.1482°, 31.1273°)", |
| " Kafr al Kurdī: (31.1684°, 31.7655°)", |
| " Fāyīd: (30.3126°, 32.3094°)", |
| " Ad Douiem: (14.0012°, 32.3116°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3843.72 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 113490.19 km²", |
| "FINAL ANSWER: Area: 113490.19 km², Perimeter: 3843.72 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": -25.76972, |
| "lon": -49.71583, |
| "name": "Lapa" |
| }, |
| { |
| "lat": -23.56439, |
| "lon": -46.61695, |
| "name": "Cambuci" |
| }, |
| { |
| "lat": -20.31944, |
| "lon": -40.33778, |
| "name": "Vitória" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 27661.84, |
| "perimeter_km": 2273.24, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Lapa: (-25.7697°, -49.7158°)", |
| " Cambuci: (-23.5644°, -46.6170°)", |
| " Vitória: (-20.3194°, -40.3378°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2273.24 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 27661.84 km²", |
| "FINAL ANSWER: Area: 27661.84 km², Perimeter: 2273.24 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": -37.60075, |
| "lon": 145.09555, |
| "name": "Mernda" |
| }, |
| { |
| "lat": -27.98941, |
| "lon": 153.33633, |
| "name": "Nerang" |
| }, |
| { |
| "lat": -30.29626, |
| "lon": 153.11351, |
| "name": "Coffs Harbour" |
| }, |
| { |
| "lat": -33.92598, |
| "lon": 151.19347, |
| "name": "Mascot" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 150859.2, |
| "perimeter_km": 2700.82, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Mernda: (-37.6007°, 145.0956°)", |
| " Nerang: (-27.9894°, 153.3363°)", |
| " Coffs Harbour: (-30.2963°, 153.1135°)", |
| " Mascot: (-33.9260°, 151.1935°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2700.82 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 150859.20 km²", |
| "FINAL ANSWER: Area: 150859.20 km², Perimeter: 2700.82 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": -33.65249, |
| "lon": 115.3455, |
| "name": "Busselton" |
| }, |
| { |
| "lat": -31.83291, |
| "lon": 115.7759, |
| "name": "Duncraig" |
| }, |
| { |
| "lat": -32.32889, |
| "lon": 115.83047, |
| "name": "Baldivis" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1617.7, |
| "perimeter_km": 415.65, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Busselton: (-33.6525°, 115.3455°)", |
| " Duncraig: (-31.8329°, 115.7759°)", |
| " Baldivis: (-32.3289°, 115.8305°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 415.65 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1617.70 km²", |
| "FINAL ANSWER: Area: 1617.70 km², Perimeter: 415.65 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 40.4246, |
| "lon": -3.68582, |
| "name": "Recoletos" |
| }, |
| { |
| "lat": 53.70324, |
| "lon": -0.87732, |
| "name": "Goole" |
| }, |
| { |
| "lat": 50.01436, |
| "lon": 8.35218, |
| "name": "Hochheim am Main" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 530338.28, |
| "perimeter_km": 3665.4, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Recoletos: (40.4246°, -3.6858°)", |
| " Goole: (53.7032°, -0.8773°)", |
| " Hochheim am Main: (50.0144°, 8.3522°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3665.40 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 530338.28 km²", |
| "FINAL ANSWER: Area: 530338.28 km², Perimeter: 3665.40 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": -19.73639, |
| "lon": -45.25222, |
| "name": "Bom Despacho" |
| }, |
| { |
| "lat": -5.52639, |
| "lon": -47.49167, |
| "name": "Imperatriz" |
| }, |
| { |
| "lat": -3.74194, |
| "lon": -47.49472, |
| "name": "Ulianópolis" |
| }, |
| { |
| "lat": -3.10056, |
| "lon": -45.03361, |
| "name": "Matinha" |
| }, |
| { |
| "lat": -3.68444, |
| "lon": -42.75028, |
| "name": "Brejo" |
| }, |
| { |
| "lat": -14.78556, |
| "lon": -39.28028, |
| "name": "Itabuna" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1011098.48, |
| "perimeter_km": 4472.09, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Bom Despacho: (-19.7364°, -45.2522°)", |
| " Imperatriz: (-5.5264°, -47.4917°)", |
| " Ulianópolis: (-3.7419°, -47.4947°)", |
| " Matinha: (-3.1006°, -45.0336°)", |
| " Brejo: (-3.6844°, -42.7503°)", |
| " Itabuna: (-14.7856°, -39.2803°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4472.09 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1011098.48 km²", |
| "FINAL ANSWER: Area: 1011098.48 km², Perimeter: 4472.09 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": -35.02692, |
| "lon": 117.88369, |
| "name": "Albany" |
| }, |
| { |
| "lat": -33.2792, |
| "lon": 115.71504, |
| "name": "Australind" |
| }, |
| { |
| "lat": -32.5269, |
| "lon": 115.7217, |
| "name": "Mandurah" |
| }, |
| { |
| "lat": -31.89578, |
| "lon": 115.76431, |
| "name": "Scarborough" |
| }, |
| { |
| "lat": -28.77897, |
| "lon": 114.61459, |
| "name": "Geraldton" |
| }, |
| { |
| "lat": -23.69748, |
| "lon": 133.88362, |
| "name": "Alice Springs" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 781108.49, |
| "perimeter_km": 4789.65, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Albany: (-35.0269°, 117.8837°)", |
| " Australind: (-33.2792°, 115.7150°)", |
| " Mandurah: (-32.5269°, 115.7217°)", |
| " Scarborough: (-31.8958°, 115.7643°)", |
| " Geraldton: (-28.7790°, 114.6146°)", |
| " Alice Springs: (-23.6975°, 133.8836°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4789.65 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 781108.49 km²", |
| "FINAL ANSWER: Area: 781108.49 km², Perimeter: 4789.65 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 35.06544, |
| "lon": 1.04945, |
| "name": "Frenda" |
| }, |
| { |
| "lat": 36.75234, |
| "lon": 4.3155, |
| "name": "Freha" |
| }, |
| { |
| "lat": 36.50361, |
| "lon": 7.44278, |
| "name": "Héliopolis" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 28970.85, |
| "perimeter_km": 1227.58, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Frenda: (35.0654°, 1.0494°)", |
| " Freha: (36.7523°, 4.3155°)", |
| " Héliopolis: (36.5036°, 7.4428°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 1227.58 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 28970.85 km²", |
| "FINAL ANSWER: Area: 28970.85 km², Perimeter: 1227.58 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 21.25993, |
| "lon": -98.78935, |
| "name": "Tamazunchale" |
| }, |
| { |
| "lat": 30.72353, |
| "lon": -95.55078, |
| "name": "Huntsville" |
| }, |
| { |
| "lat": 30.43826, |
| "lon": -84.28073, |
| "name": "Tallahassee" |
| }, |
| { |
| "lat": 22.41479, |
| "lon": -80.2931, |
| "name": "Lajas" |
| }, |
| { |
| "lat": 18.87309, |
| "lon": -71.51656, |
| "name": "Las Matas de Farfán" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1795184.93, |
| "perimeter_km": 7007.54, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Tamazunchale: (21.2599°, -98.7893°)", |
| " Huntsville: (30.7235°, -95.5508°)", |
| " Tallahassee: (30.4383°, -84.2807°)", |
| " Lajas: (22.4148°, -80.2931°)", |
| " Las Matas de Farfán: (18.8731°, -71.5166°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 7007.54 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1795184.93 km²", |
| "FINAL ANSWER: Area: 1795184.93 km², Perimeter: 7007.54 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": -25.47694, |
| "lon": -48.83444, |
| "name": "Morretes" |
| }, |
| { |
| "lat": -4.25528, |
| "lon": -43.94056, |
| "name": "Timbiras" |
| }, |
| { |
| "lat": -22.15847, |
| "lon": -43.29321, |
| "name": "Paraíba do Sul" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 575404.54, |
| "perimeter_km": 5082.4, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Morretes: (-25.4769°, -48.8344°)", |
| " Timbiras: (-4.2553°, -43.9406°)", |
| " Paraíba do Sul: (-22.1585°, -43.2932°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5082.40 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 575404.54 km²", |
| "FINAL ANSWER: Area: 575404.54 km², Perimeter: 5082.40 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": -7.1955, |
| "lon": 107.4313, |
| "name": "Banjar" |
| }, |
| { |
| "lat": 14.51691, |
| "lon": 121.2658, |
| "name": "Baras" |
| }, |
| { |
| "lat": 13.2593, |
| "lon": 123.4963, |
| "name": "Oas" |
| }, |
| { |
| "lat": 9.6531, |
| "lon": 124.3697, |
| "name": "Jagna" |
| }, |
| { |
| "lat": 8.82778, |
| "lon": 125.09972, |
| "name": "Gingoog" |
| }, |
| { |
| "lat": -0.9516, |
| "lon": 122.7875, |
| "name": "Luwuk" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1891259.35, |
| "perimeter_km": 6624.09, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Banjar: (-7.1955°, 107.4313°)", |
| " Baras: (14.5169°, 121.2658°)", |
| " Oas: (13.2593°, 123.4963°)", |
| " Jagna: (9.6531°, 124.3697°)", |
| " Gingoog: (8.8278°, 125.0997°)", |
| " Luwuk: (-0.9516°, 122.7875°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 6624.09 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1891259.35 km²", |
| "FINAL ANSWER: Area: 1891259.35 km², Perimeter: 6624.09 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": -37.74124, |
| "lon": 144.73631, |
| "name": "Caroline Springs" |
| }, |
| { |
| "lat": -36.75818, |
| "lon": 144.28024, |
| "name": "Bendigo" |
| }, |
| { |
| "lat": -33.91667, |
| "lon": 151.03333, |
| "name": "Bankstown" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 40022.13, |
| "perimeter_km": 1514.56, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Caroline Springs: (-37.7412°, 144.7363°)", |
| " Bendigo: (-36.7582°, 144.2802°)", |
| " Bankstown: (-33.9167°, 151.0333°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 1514.56 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 40022.13 km²", |
| "FINAL ANSWER: Area: 40022.13 km², Perimeter: 1514.56 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 12.70581, |
| "lon": -7.90268, |
| "name": "Sangarébougou" |
| }, |
| { |
| "lat": 13.25833, |
| "lon": -0.21306, |
| "name": "Mani" |
| }, |
| { |
| "lat": 9.04439, |
| "lon": 6.57089, |
| "name": "Lapai" |
| }, |
| { |
| "lat": 6.32485, |
| "lon": 8.11368, |
| "name": "Abakaliki" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 412283.95, |
| "perimeter_km": 3951.38, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Sangarébougou: (12.7058°, -7.9027°)", |
| " Mani: (13.2583°, -0.2131°)", |
| " Lapai: (9.0444°, 6.5709°)", |
| " Abakaliki: (6.3248°, 8.1137°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3951.38 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 412283.95 km²", |
| "FINAL ANSWER: Area: 412283.95 km², Perimeter: 3951.38 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": 17.21976, |
| "lon": -100.63032, |
| "name": "Técpan de Galeana" |
| }, |
| { |
| "lat": 19.88733, |
| "lon": -102.20636, |
| "name": "Tangancícuaro de Arista" |
| }, |
| { |
| "lat": 20.4925, |
| "lon": -103.4175, |
| "name": "Lomas del Sur" |
| }, |
| { |
| "lat": 19.90481, |
| "lon": -99.34379, |
| "name": "Tepeji del Río de Ocampo" |
| }, |
| { |
| "lat": 19.09917, |
| "lon": -98.25417, |
| "name": "Sanctorum" |
| }, |
| { |
| "lat": 18.94918, |
| "lon": -97.80379, |
| "name": "Los Reyes de Juárez" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 111248.08, |
| "perimeter_km": 1463.9, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Técpan de Galeana: (17.2198°, -100.6303°)", |
| " Tangancícuaro de Arista: (19.8873°, -102.2064°)", |
| " Lomas del Sur: (20.4925°, -103.4175°)", |
| " Tepeji del Río de Ocampo: (19.9048°, -99.3438°)", |
| " Sanctorum: (19.0992°, -98.2542°)", |
| " Los Reyes de Juárez: (18.9492°, -97.8038°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 1463.90 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 111248.08 km²", |
| "FINAL ANSWER: Area: 111248.08 km², Perimeter: 1463.90 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 30.67307, |
| "lon": -8.18087, |
| "name": "Aoulouz" |
| }, |
| { |
| "lat": 35.07465, |
| "lon": -1.22431, |
| "name": "Bensekrane" |
| }, |
| { |
| "lat": 36.73829, |
| "lon": 3.28079, |
| "name": "Rouiba" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 29227.37, |
| "perimeter_km": 2514.0, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Aoulouz: (30.6731°, -8.1809°)", |
| " Bensekrane: (35.0746°, -1.2243°)", |
| " Rouiba: (36.7383°, 3.2808°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2514.00 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 29227.37 km²", |
| "FINAL ANSWER: Area: 29227.37 km², Perimeter: 2514.00 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 9.67826, |
| "lon": 77.24951, |
| "name": "Gudalur" |
| }, |
| { |
| "lat": 20.19718, |
| "lon": 72.75035, |
| "name": "Umargām" |
| }, |
| { |
| "lat": 19.79825, |
| "lon": 85.82494, |
| "name": "Puri" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 800040.33, |
| "perimeter_km": 4085.75, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Gudalur: (9.6783°, 77.2495°)", |
| " Umargām: (20.1972°, 72.7503°)", |
| " Puri: (19.7982°, 85.8249°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4085.75 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 800040.33 km²", |
| "FINAL ANSWER: Area: 800040.33 km², Perimeter: 4085.75 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 44.91608, |
| "lon": -93.10161, |
| "name": "West Saint Paul" |
| }, |
| { |
| "lat": 40.70788, |
| "lon": -73.7868, |
| "name": "Hillside" |
| }, |
| { |
| "lat": 39.46976, |
| "lon": -76.8319, |
| "name": "Reisterstown" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 184828.39, |
| "perimeter_km": 3399.7, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " West Saint Paul: (44.9161°, -93.1016°)", |
| " Hillside: (40.7079°, -73.7868°)", |
| " Reisterstown: (39.4698°, -76.8319°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3399.70 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 184828.39 km²", |
| "FINAL ANSWER: Area: 184828.39 km², Perimeter: 3399.70 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": -38.19528, |
| "lon": 146.5415, |
| "name": "Traralgon" |
| }, |
| { |
| "lat": -37.91806, |
| "lon": 145.03544, |
| "name": "Bentleigh" |
| }, |
| { |
| "lat": -30.50123, |
| "lon": 151.66553, |
| "name": "Armidale" |
| }, |
| { |
| "lat": -33.76667, |
| "lon": 150.81667, |
| "name": "Mount Druitt" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 110690.45, |
| "perimeter_km": 2156.85, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Traralgon: (-38.1953°, 146.5415°)", |
| " Bentleigh: (-37.9181°, 145.0354°)", |
| " Armidale: (-30.5012°, 151.6655°)", |
| " Mount Druitt: (-33.7667°, 150.8167°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2156.85 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 110690.45 km²", |
| "FINAL ANSWER: Area: 110690.45 km², Perimeter: 2156.85 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 38.79269, |
| "lon": -9.1838, |
| "name": "Odivelas" |
| }, |
| { |
| "lat": 52.07417, |
| "lon": 4.35972, |
| "name": "Voorburg" |
| }, |
| { |
| "lat": 51.01122, |
| "lon": 13.82029, |
| "name": "Leuben" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 503481.59, |
| "perimeter_km": 4722.71, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Odivelas: (38.7927°, -9.1838°)", |
| " Voorburg: (52.0742°, 4.3597°)", |
| " Leuben: (51.0112°, 13.8203°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4722.71 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 503481.59 km²", |
| "FINAL ANSWER: Area: 503481.59 km², Perimeter: 4722.71 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 33.5806, |
| "lon": -112.23738, |
| "name": "Peoria" |
| }, |
| { |
| "lat": 45.68456, |
| "lon": -122.5751, |
| "name": "Five Corners" |
| }, |
| { |
| "lat": 22.18912, |
| "lon": -100.93792, |
| "name": "Soledad de Graciano Sánchez" |
| }, |
| { |
| "lat": 32.43674, |
| "lon": -111.22538, |
| "name": "Marana" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 350925.57, |
| "perimeter_km": 6556.64, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Peoria: (33.5806°, -112.2374°)", |
| " Five Corners: (45.6846°, -122.5751°)", |
| " Soledad de Graciano Sánchez: (22.1891°, -100.9379°)", |
| " Marana: (32.4367°, -111.2254°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 6556.64 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 350925.57 km²", |
| "FINAL ANSWER: Area: 350925.57 km², Perimeter: 6556.64 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": -33.2792, |
| "lon": 115.71504, |
| "name": "Australind" |
| }, |
| { |
| "lat": -33.65249, |
| "lon": 115.3455, |
| "name": "Busselton" |
| }, |
| { |
| "lat": -32.27682, |
| "lon": 115.72978, |
| "name": "Rockingham" |
| }, |
| { |
| "lat": -28.77897, |
| "lon": 114.61459, |
| "name": "Geraldton" |
| }, |
| { |
| "lat": -31.8075, |
| "lon": 115.86599, |
| "name": "Landsdale" |
| }, |
| { |
| "lat": -35.02692, |
| "lon": 117.88369, |
| "name": "Albany" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 38124.51, |
| "perimeter_km": 1654.33, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Australind: (-33.2792°, 115.7150°)", |
| " Busselton: (-33.6525°, 115.3455°)", |
| " Rockingham: (-32.2768°, 115.7298°)", |
| " Geraldton: (-28.7790°, 114.6146°)", |
| " Landsdale: (-31.8075°, 115.8660°)", |
| " Albany: (-35.0269°, 117.8837°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 1654.33 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 38124.51 km²", |
| "FINAL ANSWER: Area: 38124.51 km², Perimeter: 1654.33 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 18.56286, |
| "lon": 103.72671, |
| "name": "Borikhan" |
| }, |
| { |
| "lat": 22.35099, |
| "lon": 114.20056, |
| "name": "Tsz Ching Estate" |
| }, |
| { |
| "lat": 14.81667, |
| "lon": 120.86667, |
| "name": "Balagtas" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 597771.49, |
| "perimeter_km": 4133.72, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Borikhan: (18.5629°, 103.7267°)", |
| " Tsz Ching Estate: (22.3510°, 114.2006°)", |
| " Balagtas: (14.8167°, 120.8667°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4133.72 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 597771.49 km²", |
| "FINAL ANSWER: Area: 597771.49 km², Perimeter: 4133.72 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 53.50291, |
| "lon": -1.3458, |
| "name": "Wath upon Dearne" |
| }, |
| { |
| "lat": 51.13403, |
| "lon": 7.59075, |
| "name": "Kierspe" |
| }, |
| { |
| "lat": 47.79926, |
| "lon": 22.86255, |
| "name": "Satu Mare" |
| }, |
| { |
| "lat": 45.71667, |
| "lon": 24.15, |
| "name": "Cisnădie" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 234029.22, |
| "perimeter_km": 4090.9, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Wath upon Dearne: (53.5029°, -1.3458°)", |
| " Kierspe: (51.1340°, 7.5907°)", |
| " Satu Mare: (47.7993°, 22.8625°)", |
| " Cisnădie: (45.7167°, 24.1500°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4090.90 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 234029.22 km²", |
| "FINAL ANSWER: Area: 234029.22 km², Perimeter: 4090.90 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": -37.88461, |
| "lon": 145.29539, |
| "name": "Ferntree Gully" |
| }, |
| { |
| "lat": -27.10876, |
| "lon": 152.94907, |
| "name": "Morayfield" |
| }, |
| { |
| "lat": -27.91828, |
| "lon": 153.33275, |
| "name": "Helensvale" |
| }, |
| { |
| "lat": -33.82346, |
| "lon": 150.94607, |
| "name": "Greystanes" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 161624.81, |
| "perimeter_km": 2868.45, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Ferntree Gully: (-37.8846°, 145.2954°)", |
| " Morayfield: (-27.1088°, 152.9491°)", |
| " Helensvale: (-27.9183°, 153.3328°)", |
| " Greystanes: (-33.8235°, 150.9461°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2868.45 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 161624.81 km²", |
| "FINAL ANSWER: Area: 161624.81 km², Perimeter: 2868.45 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": -2.70924, |
| "lon": -80.24719, |
| "name": "Posorja" |
| }, |
| { |
| "lat": 4.17061, |
| "lon": -76.16641, |
| "name": "Andalucía" |
| }, |
| { |
| "lat": 6.98789, |
| "lon": -73.04953, |
| "name": "Piedecuesta" |
| }, |
| { |
| "lat": 9.4751, |
| "lon": -70.73493, |
| "name": "El Dividive" |
| }, |
| { |
| "lat": 10.15847, |
| "lon": -69.00782, |
| "name": "Urachiche" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 173036.19, |
| "perimeter_km": 3831.42, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Posorja: (-2.7092°, -80.2472°)", |
| " Andalucía: (4.1706°, -76.1664°)", |
| " Piedecuesta: (6.9879°, -73.0495°)", |
| " El Dividive: (9.4751°, -70.7349°)", |
| " Urachiche: (10.1585°, -69.0078°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3831.42 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 173036.19 km²", |
| "FINAL ANSWER: Area: 173036.19 km², Perimeter: 3831.42 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": 40.39003, |
| "lon": -3.66787, |
| "name": "San Diego" |
| }, |
| { |
| "lat": 38.76698, |
| "lon": -9.29793, |
| "name": "Cacém" |
| }, |
| { |
| "lat": 42.795, |
| "lon": -8.548, |
| "name": "Teo" |
| }, |
| { |
| "lat": 55.17719, |
| "lon": -1.56412, |
| "name": "Ashington" |
| }, |
| { |
| "lat": 51.25182, |
| "lon": 9.40747, |
| "name": "Baunatal" |
| }, |
| { |
| "lat": 43.33573, |
| "lon": 5.48201, |
| "name": "Allauch" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1415908.83, |
| "perimeter_km": 5036.55, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " San Diego: (40.3900°, -3.6679°)", |
| " Cacém: (38.7670°, -9.2979°)", |
| " Teo: (42.7950°, -8.5480°)", |
| " Ashington: (55.1772°, -1.5641°)", |
| " Baunatal: (51.2518°, 9.4075°)", |
| " Allauch: (43.3357°, 5.4820°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5036.55 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1415908.83 km²", |
| "FINAL ANSWER: Area: 1415908.83 km², Perimeter: 5036.55 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 15.53221, |
| "lon": -89.33111, |
| "name": "El Estor" |
| }, |
| { |
| "lat": 31.56017, |
| "lon": -91.40329, |
| "name": "Natchez" |
| }, |
| { |
| "lat": 41.63031, |
| "lon": -87.85394, |
| "name": "Orland Park" |
| }, |
| { |
| "lat": 27.83975, |
| "lon": -82.79121, |
| "name": "Seminole" |
| }, |
| { |
| "lat": 18.40411, |
| "lon": -66.20878, |
| "name": "Candelaria" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 2786219.89, |
| "perimeter_km": 9027.73, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " El Estor: (15.5322°, -89.3311°)", |
| " Natchez: (31.5602°, -91.4033°)", |
| " Orland Park: (41.6303°, -87.8539°)", |
| " Seminole: (27.8397°, -82.7912°)", |
| " Candelaria: (18.4041°, -66.2088°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 9027.73 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 2786219.89 km²", |
| "FINAL ANSWER: Area: 2786219.89 km², Perimeter: 9027.73 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 48.82319, |
| "lon": 1.9541, |
| "name": "Plaisir" |
| }, |
| { |
| "lat": 51.495, |
| "lon": 4.29167, |
| "name": "Bergen op Zoom" |
| }, |
| { |
| "lat": 59.38, |
| "lon": 17.80867, |
| "name": "Hässelby Villastad" |
| }, |
| { |
| "lat": 52.63598, |
| "lon": 13.20419, |
| "name": "Hennigsdorf" |
| }, |
| { |
| "lat": 48.42432, |
| "lon": 10.87273, |
| "name": "Gersthofen" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 457156.16, |
| "perimeter_km": 3514.42, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Plaisir: (48.8232°, 1.9541°)", |
| " Bergen op Zoom: (51.4950°, 4.2917°)", |
| " Hässelby Villastad: (59.3800°, 17.8087°)", |
| " Hennigsdorf: (52.6360°, 13.2042°)", |
| " Gersthofen: (48.4243°, 10.8727°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3514.42 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 457156.16 km²", |
| "FINAL ANSWER: Area: 457156.16 km², Perimeter: 3514.42 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 24.08954, |
| "lon": 38.0618, |
| "name": "Yanbu" |
| }, |
| { |
| "lat": 33.01809, |
| "lon": 36.12828, |
| "name": "Inkhil" |
| }, |
| { |
| "lat": 36.26877, |
| "lon": 50.0041, |
| "name": "Qazvin" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 663357.52, |
| "perimeter_km": 4101.17, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Yanbu: (24.0895°, 38.0618°)", |
| " Inkhil: (33.0181°, 36.1283°)", |
| " Qazvin: (36.2688°, 50.0041°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4101.17 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 663357.52 km²", |
| "FINAL ANSWER: Area: 663357.52 km², Perimeter: 4101.17 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": -22.26257, |
| "lon": 166.56621, |
| "name": "Mont-Dore" |
| }, |
| { |
| "lat": -37.68611, |
| "lon": 176.16667, |
| "name": "Tauranga" |
| }, |
| { |
| "lat": -36.88012, |
| "lon": 174.61975, |
| "name": "Henderson" |
| }, |
| { |
| "lat": -43.53333, |
| "lon": 172.63333, |
| "name": "Christchurch" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 515755.39, |
| "perimeter_km": 5298.31, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Mont-Dore: (-22.2626°, 166.5662°)", |
| " Tauranga: (-37.6861°, 176.1667°)", |
| " Henderson: (-36.8801°, 174.6198°)", |
| " Christchurch: (-43.5333°, 172.6333°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5298.31 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 515755.39 km²", |
| "FINAL ANSWER: Area: 515755.39 km², Perimeter: 5298.31 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 30.64042, |
| "lon": -8.46875, |
| "name": "Oulad Barhil" |
| }, |
| { |
| "lat": 31.6008, |
| "lon": -7.98653, |
| "name": "Méchouar-Kasba" |
| }, |
| { |
| "lat": 31.83532, |
| "lon": -7.31431, |
| "name": "Laâttaouia" |
| }, |
| { |
| "lat": 36.44788, |
| "lon": 8.4413, |
| "name": "Ghardimaou" |
| }, |
| { |
| "lat": 36.83408, |
| "lon": 10.04057, |
| "name": "Oued Lill" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 62554.62, |
| "perimeter_km": 3710.71, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Oulad Barhil: (30.6404°, -8.4688°)", |
| " Méchouar-Kasba: (31.6008°, -7.9865°)", |
| " Laâttaouia: (31.8353°, -7.3143°)", |
| " Ghardimaou: (36.4479°, 8.4413°)", |
| " Oued Lill: (36.8341°, 10.0406°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3710.71 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 62554.62 km²", |
| "FINAL ANSWER: Area: 62554.62 km², Perimeter: 3710.71 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": -37.93333, |
| "lon": 145.23333, |
| "name": "Rowville" |
| }, |
| { |
| "lat": -37.57742, |
| "lon": 144.72607, |
| "name": "Sunbury" |
| }, |
| { |
| "lat": -25.54073, |
| "lon": 152.70493, |
| "name": "Maryborough" |
| }, |
| { |
| "lat": -32.83211, |
| "lon": 151.35623, |
| "name": "Cessnock" |
| }, |
| { |
| "lat": -33.8188, |
| "lon": 151.1062, |
| "name": "Ryde" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 247173.93, |
| "perimeter_km": 3227.86, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Rowville: (-37.9333°, 145.2333°)", |
| " Sunbury: (-37.5774°, 144.7261°)", |
| " Maryborough: (-25.5407°, 152.7049°)", |
| " Cessnock: (-32.8321°, 151.3562°)", |
| " Ryde: (-33.8188°, 151.1062°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3227.86 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 247173.93 km²", |
| "FINAL ANSWER: Area: 247173.93 km², Perimeter: 3227.86 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": 5.1009, |
| "lon": 6.81411, |
| "name": "Elele" |
| }, |
| { |
| "lat": 8.43497, |
| "lon": 12.05107, |
| "name": "Ganye" |
| }, |
| { |
| "lat": 8.939, |
| "lon": 4.78227, |
| "name": "Bode Saadu" |
| }, |
| { |
| "lat": 10.26858, |
| "lon": 13.26701, |
| "name": "Mubi" |
| }, |
| { |
| "lat": 12.99809, |
| "lon": 15.73195, |
| "name": "Massakory" |
| }, |
| { |
| "lat": 9.59525, |
| "lon": 28.43493, |
| "name": "Abyei" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1199212.38, |
| "perimeter_km": 6705.7, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Elele: (5.1009°, 6.8141°)", |
| " Ganye: (8.4350°, 12.0511°)", |
| " Bode Saadu: (8.9390°, 4.7823°)", |
| " Mubi: (10.2686°, 13.2670°)", |
| " Massakory: (12.9981°, 15.7319°)", |
| " Abyei: (9.5953°, 28.4349°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 6705.70 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1199212.38 km²", |
| "FINAL ANSWER: Area: 1199212.38 km², Perimeter: 6705.70 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 30.40648, |
| "lon": -87.00553, |
| "name": "Midway" |
| }, |
| { |
| "lat": 37.97476, |
| "lon": -87.55585, |
| "name": "Evansville" |
| }, |
| { |
| "lat": 43.13339, |
| "lon": -80.7497, |
| "name": "Woodstock" |
| }, |
| { |
| "lat": 42.90395, |
| "lon": -78.69225, |
| "name": "Depew" |
| }, |
| { |
| "lat": 40.33813, |
| "lon": -79.97894, |
| "name": "Baldwin" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 414614.06, |
| "perimeter_km": 3402.49, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Midway: (30.4065°, -87.0055°)", |
| " Evansville: (37.9748°, -87.5559°)", |
| " Woodstock: (43.1334°, -80.7497°)", |
| " Depew: (42.9040°, -78.6923°)", |
| " Baldwin: (40.3381°, -79.9789°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3402.49 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 414614.06 km²", |
| "FINAL ANSWER: Area: 414614.06 km², Perimeter: 3402.49 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 37.96491, |
| "lon": 23.66511, |
| "name": "Agios Ioannis Rentis" |
| }, |
| { |
| "lat": 48.33249, |
| "lon": 19.66708, |
| "name": "Lučenec" |
| }, |
| { |
| "lat": 48.73049, |
| "lon": 37.58793, |
| "name": "Kramatorsk" |
| }, |
| { |
| "lat": 48.62831, |
| "lon": 38.56205, |
| "name": "Pervomaisk" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 829828.51, |
| "perimeter_km": 4272.1, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Agios Ioannis Rentis: (37.9649°, 23.6651°)", |
| " Lučenec: (48.3325°, 19.6671°)", |
| " Kramatorsk: (48.7305°, 37.5879°)", |
| " Pervomaisk: (48.6283°, 38.5620°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4272.10 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 829828.51 km²", |
| "FINAL ANSWER: Area: 829828.51 km², Perimeter: 4272.10 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": -38.26667, |
| "lon": 145.01667, |
| "name": "Mount Martha" |
| }, |
| { |
| "lat": -37.74981, |
| "lon": 144.9109, |
| "name": "Essendon" |
| }, |
| { |
| "lat": -37.8318, |
| "lon": 140.77919, |
| "name": "Mount Gambier" |
| }, |
| { |
| "lat": -34.75705, |
| "lon": 138.60819, |
| "name": "Paralowie" |
| }, |
| { |
| "lat": -27.98941, |
| "lon": 153.33633, |
| "name": "Nerang" |
| }, |
| { |
| "lat": -33.92399, |
| "lon": 151.22749, |
| "name": "Kingsford" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 673920.7, |
| "perimeter_km": 3827.59, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Mount Martha: (-38.2667°, 145.0167°)", |
| " Essendon: (-37.7498°, 144.9109°)", |
| " Mount Gambier: (-37.8318°, 140.7792°)", |
| " Paralowie: (-34.7570°, 138.6082°)", |
| " Nerang: (-27.9894°, 153.3363°)", |
| " Kingsford: (-33.9240°, 151.2275°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3827.59 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 673920.70 km²", |
| "FINAL ANSWER: Area: 673920.70 km², Perimeter: 3827.59 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": 4.74851, |
| "lon": -6.6363, |
| "name": "San-Pédro" |
| }, |
| { |
| "lat": 14.79032, |
| "lon": -15.90803, |
| "name": "Mbaké" |
| }, |
| { |
| "lat": 15.85615, |
| "lon": -5.79067, |
| "name": "Mbera" |
| }, |
| { |
| "lat": 12.9591, |
| "lon": -2.26075, |
| "name": "Yako" |
| }, |
| { |
| "lat": 12.25162, |
| "lon": -0.42565, |
| "name": "Pouytenga" |
| }, |
| { |
| "lat": 6.17146, |
| "lon": 7.00525, |
| "name": "Enugu-Ukwu" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1604992.09, |
| "perimeter_km": 5889.65, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " San-Pédro: (4.7485°, -6.6363°)", |
| " Mbaké: (14.7903°, -15.9080°)", |
| " Mbera: (15.8561°, -5.7907°)", |
| " Yako: (12.9591°, -2.2607°)", |
| " Pouytenga: (12.2516°, -0.4256°)", |
| " Enugu-Ukwu: (6.1715°, 7.0053°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5889.65 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1604992.09 km²", |
| "FINAL ANSWER: Area: 1604992.09 km², Perimeter: 5889.65 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": -16.7444, |
| "lon": 14.97494, |
| "name": "Xangongo" |
| }, |
| { |
| "lat": -12.35426, |
| "lon": 14.77232, |
| "name": "Balombo" |
| }, |
| { |
| "lat": -6.05255, |
| "lon": 26.9143, |
| "name": "Kabalo" |
| }, |
| { |
| "lat": -16.28333, |
| "lon": 27.48333, |
| "name": "Monze" |
| }, |
| { |
| "lat": -17.93285, |
| "lon": 25.83066, |
| "name": "Victoria Falls" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1217577.44, |
| "perimeter_km": 4546.54, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Xangongo: (-16.7444°, 14.9749°)", |
| " Balombo: (-12.3543°, 14.7723°)", |
| " Kabalo: (-6.0526°, 26.9143°)", |
| " Monze: (-16.2833°, 27.4833°)", |
| " Victoria Falls: (-17.9328°, 25.8307°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4546.54 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1217577.44 km²", |
| "FINAL ANSWER: Area: 1217577.44 km², Perimeter: 4546.54 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 40.47665, |
| "lon": -3.66852, |
| "name": "Costillares" |
| }, |
| { |
| "lat": 53.4115, |
| "lon": -2.83935, |
| "name": "Huyton" |
| }, |
| { |
| "lat": 52.08362, |
| "lon": 15.62513, |
| "name": "Sulechów" |
| }, |
| { |
| "lat": 51.05305, |
| "lon": 13.79831, |
| "name": "Blasewitz" |
| }, |
| { |
| "lat": 55.71667, |
| "lon": 37.41667, |
| "name": "Bol’shaya Setun’" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1105245.31, |
| "perimeter_km": 7919.09, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Costillares: (40.4766°, -3.6685°)", |
| " Huyton: (53.4115°, -2.8394°)", |
| " Sulechów: (52.0836°, 15.6251°)", |
| " Blasewitz: (51.0530°, 13.7983°)", |
| " Bol’shaya Setun’: (55.7167°, 37.4167°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 7919.09 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1105245.31 km²", |
| "FINAL ANSWER: Area: 1105245.31 km², Perimeter: 7919.09 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": -21.96917, |
| "lon": -46.79806, |
| "name": "São João da Boa Vista" |
| }, |
| { |
| "lat": -25.44472, |
| "lon": -49.1925, |
| "name": "Pinhais" |
| }, |
| { |
| "lat": -20.21111, |
| "lon": -50.92583, |
| "name": "Santa Fé do Sul" |
| }, |
| { |
| "lat": -7.93333, |
| "lon": -39.29583, |
| "name": "Serrita" |
| }, |
| { |
| "lat": -17.21861, |
| "lon": -42.59028, |
| "name": "Minas Novas" |
| }, |
| { |
| "lat": -20.54139, |
| "lon": -44.635, |
| "name": "Carmópolis de Minas" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 672532.13, |
| "perimeter_km": 4711.99, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " São João da Boa Vista: (-21.9692°, -46.7981°)", |
| " Pinhais: (-25.4447°, -49.1925°)", |
| " Santa Fé do Sul: (-20.2111°, -50.9258°)", |
| " Serrita: (-7.9333°, -39.2958°)", |
| " Minas Novas: (-17.2186°, -42.5903°)", |
| " Carmópolis de Minas: (-20.5414°, -44.6350°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4711.99 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 672532.13 km²", |
| "FINAL ANSWER: Area: 672532.13 km², Perimeter: 4711.99 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": -37.8, |
| "lon": 144.9, |
| "name": "Footscray" |
| }, |
| { |
| "lat": -27.63917, |
| "lon": 153.10944, |
| "name": "Logan City" |
| }, |
| { |
| "lat": -33.92399, |
| "lon": 151.22749, |
| "name": "Kingsford" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 152862.71, |
| "perimeter_km": 2800.78, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Footscray: (-37.8000°, 144.9000°)", |
| " Logan City: (-27.6392°, 153.1094°)", |
| " Kingsford: (-33.9240°, 151.2275°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2800.78 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 152862.71 km²", |
| "FINAL ANSWER: Area: 152862.71 km², Perimeter: 2800.78 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 50.93182, |
| "lon": 6.99469, |
| "name": "Humboldtkolonie" |
| }, |
| { |
| "lat": 53.5476, |
| "lon": 8.10395, |
| "name": "Wilhelmshaven" |
| }, |
| { |
| "lat": 53.86639, |
| "lon": 34.44778, |
| "name": "Lyudinovo" |
| }, |
| { |
| "lat": 48.51716, |
| "lon": 34.60617, |
| "name": "Kamyanske" |
| }, |
| { |
| "lat": 46.81601, |
| "lon": 33.47862, |
| "name": "Kakhovka" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1002581.71, |
| "perimeter_km": 4805.45, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Humboldtkolonie: (50.9318°, 6.9947°)", |
| " Wilhelmshaven: (53.5476°, 8.1039°)", |
| " Lyudinovo: (53.8664°, 34.4478°)", |
| " Kamyanske: (48.5172°, 34.6062°)", |
| " Kakhovka: (46.8160°, 33.4786°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4805.45 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1002581.71 km²", |
| "FINAL ANSWER: Area: 1002581.71 km², Perimeter: 4805.45 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 30.26224, |
| "lon": -9.50377, |
| "name": "Ben Jerrar" |
| }, |
| { |
| "lat": 33.34499, |
| "lon": -3.70387, |
| "name": "Outat Oulad Al Haj" |
| }, |
| { |
| "lat": 36.78567, |
| "lon": 4.06273, |
| "name": "Makouda" |
| }, |
| { |
| "lat": 36.75472, |
| "lon": 6.2725, |
| "name": "El Milia" |
| }, |
| { |
| "lat": 26.52161, |
| "lon": 13.01072, |
| "name": "Al Ghurayfah" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1123258.36, |
| "perimeter_km": 5187.43, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Ben Jerrar: (30.2622°, -9.5038°)", |
| " Outat Oulad Al Haj: (33.3450°, -3.7039°)", |
| " Makouda: (36.7857°, 4.0627°)", |
| " El Milia: (36.7547°, 6.2725°)", |
| " Al Ghurayfah: (26.5216°, 13.0107°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5187.43 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1123258.36 km²", |
| "FINAL ANSWER: Area: 1123258.36 km², Perimeter: 5187.43 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 8.13373, |
| "lon": 4.24014, |
| "name": "Ogbomoso" |
| }, |
| { |
| "lat": 6.76051, |
| "lon": -1.59402, |
| "name": "Ahwiaa" |
| }, |
| { |
| "lat": 11.13417, |
| "lon": 2.93861, |
| "name": "Kandi" |
| }, |
| { |
| "lat": 12.47554, |
| "lon": 15.43647, |
| "name": "Massaguet" |
| }, |
| { |
| "lat": 10.28969, |
| "lon": 11.16729, |
| "name": "Gombe" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 398243.2, |
| "perimeter_km": 4047.47, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Ogbomoso: (8.1337°, 4.2401°)", |
| " Ahwiaa: (6.7605°, -1.5940°)", |
| " Kandi: (11.1342°, 2.9386°)", |
| " Massaguet: (12.4755°, 15.4365°)", |
| " Gombe: (10.2897°, 11.1673°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4047.47 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 398243.20 km²", |
| "FINAL ANSWER: Area: 398243.20 km², Perimeter: 4047.47 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": -37.76667, |
| "lon": 145.0, |
| "name": "Northcote" |
| }, |
| { |
| "lat": -34.75705, |
| "lon": 138.60819, |
| "name": "Paralowie" |
| }, |
| { |
| "lat": -28.21901, |
| "lon": 152.03438, |
| "name": "Warwick" |
| }, |
| { |
| "lat": -27.3171, |
| "lon": 153.03097, |
| "name": "Bracken Ridge" |
| }, |
| { |
| "lat": -33.77271, |
| "lon": 151.08184, |
| "name": "Epping" |
| }, |
| { |
| "lat": -34.4279, |
| "lon": 150.89268, |
| "name": "Wollongong city centre" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 599307.54, |
| "perimeter_km": 3730.7, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Northcote: (-37.7667°, 145.0000°)", |
| " Paralowie: (-34.7570°, 138.6082°)", |
| " Warwick: (-28.2190°, 152.0344°)", |
| " Bracken Ridge: (-27.3171°, 153.0310°)", |
| " Epping: (-33.7727°, 151.0818°)", |
| " Wollongong city centre: (-34.4279°, 150.8927°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3730.70 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 599307.54 km²", |
| "FINAL ANSWER: Area: 599307.54 km², Perimeter: 3730.70 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": -16.02511, |
| "lon": -48.07121, |
| "name": "Gama" |
| }, |
| { |
| "lat": -2.88, |
| "lon": -52.01, |
| "name": "Vitória do Xingu" |
| }, |
| { |
| "lat": -1.74833, |
| "lon": -52.23833, |
| "name": "Porto de Moz" |
| }, |
| { |
| "lat": -5.61278, |
| "lon": -38.76694, |
| "name": "Jaguaretama" |
| }, |
| { |
| "lat": -7.64265, |
| "lon": -47.21738, |
| "name": "Santa Luzia" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1525527.83, |
| "perimeter_km": 5104.27, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Gama: (-16.0251°, -48.0712°)", |
| " Vitória do Xingu: (-2.8800°, -52.0100°)", |
| " Porto de Moz: (-1.7483°, -52.2383°)", |
| " Jaguaretama: (-5.6128°, -38.7669°)", |
| " Santa Luzia: (-7.6426°, -47.2174°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5104.27 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1525527.83 km²", |
| "FINAL ANSWER: Area: 1525527.83 km², Perimeter: 5104.27 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 30.89315, |
| "lon": 49.40787, |
| "name": "Rāmshīr" |
| }, |
| { |
| "lat": 37.41853, |
| "lon": 66.04358, |
| "name": "Qarqīn" |
| }, |
| { |
| "lat": 21.32855, |
| "lon": 71.02645, |
| "name": "Dhāri" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1579811.76, |
| "perimeter_km": 5943.18, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Rāmshīr: (30.8931°, 49.4079°)", |
| " Qarqīn: (37.4185°, 66.0436°)", |
| " Dhāri: (21.3285°, 71.0264°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5943.18 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1579811.76 km²", |
| "FINAL ANSWER: Area: 1579811.76 km², Perimeter: 5943.18 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": -9.3, |
| "lon": 32.76667, |
| "name": "Tunduma" |
| }, |
| { |
| "lat": -2.63778, |
| "lon": 31.76694, |
| "name": "Chato" |
| }, |
| { |
| "lat": -3.0804, |
| "lon": 29.391, |
| "name": "Bubanza" |
| }, |
| { |
| "lat": 1.43139, |
| "lon": 33.77722, |
| "name": "Ngora" |
| }, |
| { |
| "lat": 10.45, |
| "lon": 38.2, |
| "name": "Bichena" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 600333.33, |
| "perimeter_km": 5109.4, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Tunduma: (-9.3000°, 32.7667°)", |
| " Chato: (-2.6378°, 31.7669°)", |
| " Bubanza: (-3.0804°, 29.3910°)", |
| " Ngora: (1.4314°, 33.7772°)", |
| " Bichena: (10.4500°, 38.2000°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5109.40 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 600333.33 km²", |
| "FINAL ANSWER: Area: 600333.33 km², Perimeter: 5109.40 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": 35.94204, |
| "lon": -95.88332, |
| "name": "Bixby" |
| }, |
| { |
| "lat": 41.6764, |
| "lon": -91.58045, |
| "name": "Coralville" |
| }, |
| { |
| "lat": 42.93173, |
| "lon": -76.56605, |
| "name": "Auburn" |
| }, |
| { |
| "lat": 40.40816, |
| "lon": -74.35432, |
| "name": "South Old Bridge" |
| }, |
| { |
| "lat": 39.65287, |
| "lon": -78.76252, |
| "name": "Cumberland" |
| }, |
| { |
| "lat": 36.09986, |
| "lon": -80.24422, |
| "name": "Winston-Salem" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 941363.77, |
| "perimeter_km": 4520.25, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Bixby: (35.9420°, -95.8833°)", |
| " Coralville: (41.6764°, -91.5804°)", |
| " Auburn: (42.9317°, -76.5661°)", |
| " South Old Bridge: (40.4082°, -74.3543°)", |
| " Cumberland: (39.6529°, -78.7625°)", |
| " Winston-Salem: (36.0999°, -80.2442°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4520.25 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 941363.77 km²", |
| "FINAL ANSWER: Area: 941363.77 km², Perimeter: 4520.25 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": 31.73443, |
| "lon": -7.00505, |
| "name": "Demnate" |
| }, |
| { |
| "lat": 34.89638, |
| "lon": 3.48543, |
| "name": "Dar Chioukh" |
| }, |
| { |
| "lat": 36.13516, |
| "lon": 2.91085, |
| "name": "Berrouaghia" |
| }, |
| { |
| "lat": 35.85451, |
| "lon": 5.29053, |
| "name": "Salah Bey" |
| }, |
| { |
| "lat": 36.89479, |
| "lon": 10.18604, |
| "name": "La Gazelle" |
| }, |
| { |
| "lat": 34.3827, |
| "lon": 8.15549, |
| "name": "Ar Rudayyif" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 333200.54, |
| "perimeter_km": 3628.35, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Demnate: (31.7344°, -7.0050°)", |
| " Dar Chioukh: (34.8964°, 3.4854°)", |
| " Berrouaghia: (36.1352°, 2.9108°)", |
| " Salah Bey: (35.8545°, 5.2905°)", |
| " La Gazelle: (36.8948°, 10.1860°)", |
| " Ar Rudayyif: (34.3827°, 8.1555°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3628.35 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 333200.54 km²", |
| "FINAL ANSWER: Area: 333200.54 km², Perimeter: 3628.35 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": -38.19528, |
| "lon": 146.5415, |
| "name": "Traralgon" |
| }, |
| { |
| "lat": -37.87709, |
| "lon": 145.12939, |
| "name": "Mount Waverley" |
| }, |
| { |
| "lat": -32.92953, |
| "lon": 151.7801, |
| "name": "Newcastle" |
| }, |
| { |
| "lat": -34.75155, |
| "lon": 149.72086, |
| "name": "Goulburn" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 53311.44, |
| "perimeter_km": 1699.0, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Traralgon: (-38.1953°, 146.5415°)", |
| " Mount Waverley: (-37.8771°, 145.1294°)", |
| " Newcastle: (-32.9295°, 151.7801°)", |
| " Goulburn: (-34.7516°, 149.7209°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 1699.00 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 53311.44 km²", |
| "FINAL ANSWER: Area: 53311.44 km², Perimeter: 1699.00 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": -19.8, |
| "lon": -41.43833, |
| "name": "Mutum" |
| }, |
| { |
| "lat": -3.54306, |
| "lon": -43.91583, |
| "name": "Vargem Grande" |
| }, |
| { |
| "lat": -10.83444, |
| "lon": -38.53583, |
| "name": "Ribeira do Pombal" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 425409.61, |
| "perimeter_km": 3876.38, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Mutum: (-19.8000°, -41.4383°)", |
| " Vargem Grande: (-3.5431°, -43.9158°)", |
| " Ribeira do Pombal: (-10.8344°, -38.5358°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3876.38 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 425409.61 km²", |
| "FINAL ANSWER: Area: 425409.61 km², Perimeter: 3876.38 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 37.21807, |
| "lon": 28.3665, |
| "name": "Muğla" |
| }, |
| { |
| "lat": 40.89105, |
| "lon": 26.90201, |
| "name": "Malkara" |
| }, |
| { |
| "lat": 39.20762, |
| "lon": 46.40678, |
| "name": "Kapan" |
| }, |
| { |
| "lat": 36.68489, |
| "lon": 52.51917, |
| "name": "Fereydūn Kenār" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 569455.65, |
| "perimeter_km": 4840.74, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Muğla: (37.2181°, 28.3665°)", |
| " Malkara: (40.8910°, 26.9020°)", |
| " Kapan: (39.2076°, 46.4068°)", |
| " Fereydūn Kenār: (36.6849°, 52.5192°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4840.74 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 569455.65 km²", |
| "FINAL ANSWER: Area: 569455.65 km², Perimeter: 4840.74 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 45.07176, |
| "lon": 7.67919, |
| "name": "Centro" |
| }, |
| { |
| "lat": 50.704, |
| "lon": 7.054, |
| "name": "Bonn Hardtberg" |
| }, |
| { |
| "lat": 47.88238, |
| "lon": 10.62192, |
| "name": "Kaufbeuren" |
| }, |
| { |
| "lat": 38.22008, |
| "lon": 15.24023, |
| "name": "Milazzo" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 261272.77, |
| "perimeter_km": 3158.65, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Centro: (45.0718°, 7.6792°)", |
| " Bonn Hardtberg: (50.7040°, 7.0540°)", |
| " Kaufbeuren: (47.8824°, 10.6219°)", |
| " Milazzo: (38.2201°, 15.2402°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3158.65 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 261272.77 km²", |
| "FINAL ANSWER: Area: 261272.77 km², Perimeter: 3158.65 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 36.97412, |
| "lon": -122.0308, |
| "name": "Santa Cruz" |
| }, |
| { |
| "lat": 37.34772, |
| "lon": -120.60908, |
| "name": "Atwater" |
| }, |
| { |
| "lat": 39.92054, |
| "lon": -105.08665, |
| "name": "Broomfield" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1675.77, |
| "perimeter_km": 3018.07, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Santa Cruz: (36.9741°, -122.0308°)", |
| " Atwater: (37.3477°, -120.6091°)", |
| " Broomfield: (39.9205°, -105.0867°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3018.07 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1675.77 km²", |
| "FINAL ANSWER: Area: 1675.77 km², Perimeter: 3018.07 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": -41.51603, |
| "lon": 173.9528, |
| "name": "Blenheim" |
| }, |
| { |
| "lat": -39.06667, |
| "lon": 174.08333, |
| "name": "New Plymouth" |
| }, |
| { |
| "lat": -36.96807, |
| "lon": 174.79875, |
| "name": "Mangere" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 7395.31, |
| "perimeter_km": 1025.12, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Blenheim: (-41.5160°, 173.9528°)", |
| " New Plymouth: (-39.0667°, 174.0833°)", |
| " Mangere: (-36.9681°, 174.7988°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 1025.12 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 7395.31 km²", |
| "FINAL ANSWER: Area: 7395.31 km², Perimeter: 1025.12 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 17.7, |
| "lon": 83.21667, |
| "name": "Gajuwaka" |
| }, |
| { |
| "lat": 24.33353, |
| "lon": 93.66999, |
| "name": "Churāchāndpur" |
| }, |
| { |
| "lat": 1.36259, |
| "lon": 109.30093, |
| "name": "Kota Sambas" |
| }, |
| { |
| "lat": 7.90963, |
| "lon": 98.40248, |
| "name": "Ban Ratsada" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 2160935.06, |
| "perimeter_km": 7750.45, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Gajuwaka: (17.7000°, 83.2167°)", |
| " Churāchāndpur: (24.3335°, 93.6700°)", |
| " Kota Sambas: (1.3626°, 109.3009°)", |
| " Ban Ratsada: (7.9096°, 98.4025°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 7750.45 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 2160935.06 km²", |
| "FINAL ANSWER: Area: 2160935.06 km², Perimeter: 7750.45 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 46.18096, |
| "lon": 6.13921, |
| "name": "Carouge" |
| }, |
| { |
| "lat": 53.07738, |
| "lon": 7.40444, |
| "name": "Papenburg" |
| }, |
| { |
| "lat": 52.30141, |
| "lon": 13.633, |
| "name": "Königs Wusterhausen" |
| }, |
| { |
| "lat": 52.0814, |
| "lon": 21.02397, |
| "name": "Piaseczno" |
| }, |
| { |
| "lat": 41.68573, |
| "lon": 12.77753, |
| "name": "Velletri" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 781120.12, |
| "perimeter_km": 3746.97, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Carouge: (46.1810°, 6.1392°)", |
| " Papenburg: (53.0774°, 7.4044°)", |
| " Königs Wusterhausen: (52.3014°, 13.6330°)", |
| " Piaseczno: (52.0814°, 21.0240°)", |
| " Velletri: (41.6857°, 12.7775°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3746.97 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 781120.12 km²", |
| "FINAL ANSWER: Area: 781120.12 km², Perimeter: 3746.97 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": -37.81819, |
| "lon": 145.00176, |
| "name": "Richmond" |
| }, |
| { |
| "lat": -27.08465, |
| "lon": 152.9511, |
| "name": "Caboolture" |
| }, |
| { |
| "lat": -27.54333, |
| "lon": 153.20287, |
| "name": "Capalaba" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 33151.62, |
| "perimeter_km": 2837.8, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Richmond: (-37.8182°, 145.0018°)", |
| " Caboolture: (-27.0846°, 152.9511°)", |
| " Capalaba: (-27.5433°, 153.2029°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2837.80 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 33151.62 km²", |
| "FINAL ANSWER: Area: 33151.62 km², Perimeter: 2837.80 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": -27.31472, |
| "lon": -48.55917, |
| "name": "Governador Celso Ramos" |
| }, |
| { |
| "lat": -27.25806, |
| "lon": -49.93389, |
| "name": "Pouso Redondo" |
| }, |
| { |
| "lat": -22.88333, |
| "lon": -43.10361, |
| "name": "Niterói" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 34296.98, |
| "perimeter_km": 1716.02, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Governador Celso Ramos: (-27.3147°, -48.5592°)", |
| " Pouso Redondo: (-27.2581°, -49.9339°)", |
| " Niterói: (-22.8833°, -43.1036°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 1716.02 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 34296.98 km²", |
| "FINAL ANSWER: Area: 34296.98 km², Perimeter: 1716.02 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 12.42602, |
| "lon": 75.7382, |
| "name": "Madikeri" |
| }, |
| { |
| "lat": 24.13524, |
| "lon": 74.04442, |
| "name": "Sālūmbar" |
| }, |
| { |
| "lat": 25.69515, |
| "lon": 81.92336, |
| "name": "Mau Aimma" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 534477.48, |
| "perimeter_km": 3738.8, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Madikeri: (12.4260°, 75.7382°)", |
| " Sālūmbar: (24.1352°, 74.0444°)", |
| " Mau Aimma: (25.6952°, 81.9234°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3738.80 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 534477.48 km²", |
| "FINAL ANSWER: Area: 534477.48 km², Perimeter: 3738.80 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": -37.88214, |
| "lon": 144.98215, |
| "name": "Elwood" |
| }, |
| { |
| "lat": -38.02388, |
| "lon": 144.40617, |
| "name": "Lara" |
| }, |
| { |
| "lat": -27.58333, |
| "lon": 153.1, |
| "name": "Eight Mile Plains" |
| }, |
| { |
| "lat": -31.91099, |
| "lon": 152.45387, |
| "name": "Taree" |
| }, |
| { |
| "lat": -35.41647, |
| "lon": 149.06954, |
| "name": "Tuggeranong Administrative District" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 182331.68, |
| "perimeter_km": 2909.7, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Elwood: (-37.8821°, 144.9821°)", |
| " Lara: (-38.0239°, 144.4062°)", |
| " Eight Mile Plains: (-27.5833°, 153.1000°)", |
| " Taree: (-31.9110°, 152.4539°)", |
| " Tuggeranong Administrative District: (-35.4165°, 149.0695°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2909.70 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 182331.68 km²", |
| "FINAL ANSWER: Area: 182331.68 km², Perimeter: 2909.70 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": -27.50766, |
| "lon": -58.55625, |
| "name": "San Luis del Palmar" |
| }, |
| { |
| "lat": -23.28167, |
| "lon": -46.74528, |
| "name": "Francisco Morato" |
| }, |
| { |
| "lat": -24.52611, |
| "lon": -49.94861, |
| "name": "Piraí do Sul" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1612.83, |
| "perimeter_km": 2550.63, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " San Luis del Palmar: (-27.5077°, -58.5562°)", |
| " Francisco Morato: (-23.2817°, -46.7453°)", |
| " Piraí do Sul: (-24.5261°, -49.9486°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2550.63 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1612.83 km²", |
| "FINAL ANSWER: Area: 1612.83 km², Perimeter: 2550.63 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 16.36491, |
| "lon": 77.35863, |
| "name": "Shaktinagar" |
| }, |
| { |
| "lat": 33.46659, |
| "lon": 76.88488, |
| "name": "Padam" |
| }, |
| { |
| "lat": 38.18867, |
| "lon": 77.27075, |
| "name": "Zepu" |
| }, |
| { |
| "lat": 36.8545, |
| "lon": 81.66425, |
| "name": "Mugala" |
| }, |
| { |
| "lat": 23.37583, |
| "lon": 93.65389, |
| "name": "Tedim" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 2261899.73, |
| "perimeter_km": 6602.74, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Shaktinagar: (16.3649°, 77.3586°)", |
| " Padam: (33.4666°, 76.8849°)", |
| " Zepu: (38.1887°, 77.2708°)", |
| " Mugala: (36.8545°, 81.6642°)", |
| " Tedim: (23.3758°, 93.6539°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 6602.74 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 2261899.73 km²", |
| "FINAL ANSWER: Area: 2261899.73 km², Perimeter: 6602.74 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 32.96179, |
| "lon": -96.82917, |
| "name": "Addison" |
| }, |
| { |
| "lat": 43.59781, |
| "lon": -84.76751, |
| "name": "Mount Pleasant" |
| }, |
| { |
| "lat": 45.50884, |
| "lon": -73.58781, |
| "name": "Montréal" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 331768.91, |
| "perimeter_km": 4915.64, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Addison: (32.9618°, -96.8292°)", |
| " Mount Pleasant: (43.5978°, -84.7675°)", |
| " Montréal: (45.5088°, -73.5878°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4915.64 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 331768.91 km²", |
| "FINAL ANSWER: Area: 331768.91 km², Perimeter: 4915.64 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": 32.5064, |
| "lon": 34.92087, |
| "name": "Or Akiva" |
| }, |
| { |
| "lat": 39.64917, |
| "lon": 27.88611, |
| "name": "Balıkesir" |
| }, |
| { |
| "lat": 40.76499, |
| "lon": 29.92928, |
| "name": "İzmit" |
| }, |
| { |
| "lat": 38.6908, |
| "lon": 35.5538, |
| "name": "Talas" |
| }, |
| { |
| "lat": 40.75972, |
| "lon": 36.3225, |
| "name": "Taşova" |
| }, |
| { |
| "lat": 31.01547, |
| "lon": 47.43362, |
| "name": "Al Qurnah" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 848641.41, |
| "perimeter_km": 4666.71, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Or Akiva: (32.5064°, 34.9209°)", |
| " Balıkesir: (39.6492°, 27.8861°)", |
| " İzmit: (40.7650°, 29.9293°)", |
| " Talas: (38.6908°, 35.5538°)", |
| " Taşova: (40.7597°, 36.3225°)", |
| " Al Qurnah: (31.0155°, 47.4336°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4666.71 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 848641.41 km²", |
| "FINAL ANSWER: Area: 848641.41 km², Perimeter: 4666.71 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": -38.38176, |
| "lon": 142.48799, |
| "name": "Warrnambool" |
| }, |
| { |
| "lat": -34.91119, |
| "lon": 138.70735, |
| "name": "Adelaide Hills" |
| }, |
| { |
| "lat": -33.91938, |
| "lon": 150.92588, |
| "name": "Liverpool" |
| }, |
| { |
| "lat": -36.12179, |
| "lon": 146.88809, |
| "name": "Wodonga" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 230727.33, |
| "perimeter_km": 2543.07, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Warrnambool: (-38.3818°, 142.4880°)", |
| " Adelaide Hills: (-34.9112°, 138.7073°)", |
| " Liverpool: (-33.9194°, 150.9259°)", |
| " Wodonga: (-36.1218°, 146.8881°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2543.07 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 230727.33 km²", |
| "FINAL ANSWER: Area: 230727.33 km², Perimeter: 2543.07 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": -41.13827, |
| "lon": 175.0502, |
| "name": "Upper Hutt" |
| }, |
| { |
| "lat": -36.88745, |
| "lon": 174.77059, |
| "name": "Epsom" |
| }, |
| { |
| "lat": -37.78821, |
| "lon": 175.2902, |
| "name": "Hamilton East" |
| }, |
| { |
| "lat": -40.95972, |
| "lon": 175.6575, |
| "name": "Masterton" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 18911.08, |
| "perimeter_km": 992.2, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Upper Hutt: (-41.1383°, 175.0502°)", |
| " Epsom: (-36.8875°, 174.7706°)", |
| " Hamilton East: (-37.7882°, 175.2902°)", |
| " Masterton: (-40.9597°, 175.6575°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 992.20 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 18911.08 km²", |
| "FINAL ANSWER: Area: 18911.08 km², Perimeter: 992.20 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 42.97839, |
| "lon": -78.79976, |
| "name": "Amherst" |
| }, |
| { |
| "lat": 41.66121, |
| "lon": -72.77954, |
| "name": "New Britain" |
| }, |
| { |
| "lat": 40.72149, |
| "lon": -73.7693, |
| "name": "Terrace Heights" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 32294.24, |
| "perimeter_km": 1135.65, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Amherst: (42.9784°, -78.7998°)", |
| " New Britain: (41.6612°, -72.7795°)", |
| " Terrace Heights: (40.7215°, -73.7693°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 1135.65 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 32294.24 km²", |
| "FINAL ANSWER: Area: 32294.24 km², Perimeter: 1135.65 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": -10.98303, |
| "lon": 26.7384, |
| "name": "Likasi" |
| }, |
| { |
| "lat": -4.36667, |
| "lon": 35.08333, |
| "name": "Basotu" |
| }, |
| { |
| "lat": -11.01863, |
| "lon": 33.85746, |
| "name": "Rumphi" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 287809.36, |
| "perimeter_km": 2706.18, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Likasi: (-10.9830°, 26.7384°)", |
| " Basotu: (-4.3667°, 35.0833°)", |
| " Rumphi: (-11.0186°, 33.8575°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2706.18 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 287809.36 km²", |
| "FINAL ANSWER: Area: 287809.36 km², Perimeter: 2706.18 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 39.54595, |
| "lon": -0.57069, |
| "name": "Ribarroja del Turia" |
| }, |
| { |
| "lat": 56.33871, |
| "lon": -2.79902, |
| "name": "Saint Andrews" |
| }, |
| { |
| "lat": 52.234, |
| "lon": 4.44474, |
| "name": "Noordwijk-Binnen" |
| }, |
| { |
| "lat": 50.14952, |
| "lon": 18.84215, |
| "name": "Łaziska Górne" |
| }, |
| { |
| "lat": 40.57762, |
| "lon": 17.03812, |
| "name": "Palagiano" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1973145.81, |
| "perimeter_km": 6130.89, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Ribarroja del Turia: (39.5459°, -0.5707°)", |
| " Saint Andrews: (56.3387°, -2.7990°)", |
| " Noordwijk-Binnen: (52.2340°, 4.4447°)", |
| " Łaziska Górne: (50.1495°, 18.8422°)", |
| " Palagiano: (40.5776°, 17.0381°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 6130.89 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1973145.81 km²", |
| "FINAL ANSWER: Area: 1973145.81 km², Perimeter: 6130.89 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 50.31505, |
| "lon": 17.38355, |
| "name": "Głuchołazy" |
| }, |
| { |
| "lat": 58.14, |
| "lon": 52.65619, |
| "name": "Glazov" |
| }, |
| { |
| "lat": 51.88056, |
| "lon": 45.00609, |
| "name": "Atkarsk" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 743305.95, |
| "perimeter_km": 5192.33, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Głuchołazy: (50.3150°, 17.3835°)", |
| " Glazov: (58.1400°, 52.6562°)", |
| " Atkarsk: (51.8806°, 45.0061°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5192.33 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 743305.95 km²", |
| "FINAL ANSWER: Area: 743305.95 km², Perimeter: 5192.33 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": -3.54964, |
| "lon": 143.63229, |
| "name": "Wewak" |
| }, |
| { |
| "lat": 13.48773, |
| "lon": 144.78138, |
| "name": "Tamuning-Tumon-Harmon Village" |
| }, |
| { |
| "lat": 15.21233, |
| "lon": 145.7545, |
| "name": "Saipan" |
| }, |
| { |
| "lat": 6.92477, |
| "lon": 158.16109, |
| "name": "Palikir" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1634342.25, |
| "perimeter_km": 5743.03, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Wewak: (-3.5496°, 143.6323°)", |
| " Tamuning-Tumon-Harmon Village: (13.4877°, 144.7814°)", |
| " Saipan: (15.2123°, 145.7545°)", |
| " Palikir: (6.9248°, 158.1611°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5743.03 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1634342.25 km²", |
| "FINAL ANSWER: Area: 1634342.25 km², Perimeter: 5743.03 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 4.5141, |
| "lon": 103.4483, |
| "name": "Kertih" |
| }, |
| { |
| "lat": 17.3072, |
| "lon": 102.18886, |
| "name": "Na Klang" |
| }, |
| { |
| "lat": -6.7559, |
| "lon": 111.038, |
| "name": "Pati" |
| }, |
| { |
| "lat": -6.17806, |
| "lon": 106.63, |
| "name": "Tangerang" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 805351.74, |
| "perimeter_km": 6007.55, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Kertih: (4.5141°, 103.4483°)", |
| " Na Klang: (17.3072°, 102.1889°)", |
| " Pati: (-6.7559°, 111.0380°)", |
| " Tangerang: (-6.1781°, 106.6300°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 6007.55 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 805351.74 km²", |
| "FINAL ANSWER: Area: 805351.74 km², Perimeter: 6007.55 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 33.71372, |
| "lon": -117.76091, |
| "name": "Northwood" |
| }, |
| { |
| "lat": 34.19731, |
| "lon": -118.64398, |
| "name": "West Hills" |
| }, |
| { |
| "lat": 49.24966, |
| "lon": -123.11934, |
| "name": "Vancouver" |
| }, |
| { |
| "lat": 52.13238, |
| "lon": -106.66892, |
| "name": "Saskatoon" |
| }, |
| { |
| "lat": 33.4356, |
| "lon": -112.3496, |
| "name": "Avondale" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1673809.22, |
| "perimeter_km": 5641.27, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Northwood: (33.7137°, -117.7609°)", |
| " West Hills: (34.1973°, -118.6440°)", |
| " Vancouver: (49.2497°, -123.1193°)", |
| " Saskatoon: (52.1324°, -106.6689°)", |
| " Avondale: (33.4356°, -112.3496°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5641.27 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1673809.22 km²", |
| "FINAL ANSWER: Area: 1673809.22 km², Perimeter: 5641.27 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 10.96209, |
| "lon": -3.24967, |
| "name": "Diébougou" |
| }, |
| { |
| "lat": 11.31755, |
| "lon": -5.66654, |
| "name": "Sikasso" |
| }, |
| { |
| "lat": 10.13366, |
| "lon": 14.70748, |
| "name": "Guidiguis" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 35723.4, |
| "perimeter_km": 4460.84, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Diébougou: (10.9621°, -3.2497°)", |
| " Sikasso: (11.3176°, -5.6665°)", |
| " Guidiguis: (10.1337°, 14.7075°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4460.84 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 35723.40 km²", |
| "FINAL ANSWER: Area: 35723.40 km², Perimeter: 4460.84 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 51.2099, |
| "lon": 4.03651, |
| "name": "Stekene" |
| }, |
| { |
| "lat": 51.91917, |
| "lon": 5.84167, |
| "name": "Elst" |
| }, |
| { |
| "lat": 52.11457, |
| "lon": 8.67343, |
| "name": "Herford" |
| }, |
| { |
| "lat": 46.88152, |
| "lon": 17.44117, |
| "name": "Tapolca" |
| }, |
| { |
| "lat": 43.29789, |
| "lon": 13.45293, |
| "name": "Macerata" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 396884.32, |
| "perimeter_km": 2837.17, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Stekene: (51.2099°, 4.0365°)", |
| " Elst: (51.9192°, 5.8417°)", |
| " Herford: (52.1146°, 8.6734°)", |
| " Tapolca: (46.8815°, 17.4412°)", |
| " Macerata: (43.2979°, 13.4529°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2837.17 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 396884.32 km²", |
| "FINAL ANSWER: Area: 396884.32 km², Perimeter: 2837.17 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": 34.87045, |
| "lon": -1.42319, |
| "name": "Beni Mester" |
| }, |
| { |
| "lat": 36.10124, |
| "lon": 1.19949, |
| "name": "Oued Sly" |
| }, |
| { |
| "lat": 36.65, |
| "lon": 4.77361, |
| "name": "el hed" |
| }, |
| { |
| "lat": 36.51611, |
| "lon": 6.32722, |
| "name": "Grarem" |
| }, |
| { |
| "lat": 32.63278, |
| "lon": 12.87361, |
| "name": "An Nāşirīyah" |
| }, |
| { |
| "lat": 34.72224, |
| "lon": 5.37845, |
| "name": "Tolga" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 274570.84, |
| "perimeter_km": 2830.08, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Beni Mester: (34.8704°, -1.4232°)", |
| " Oued Sly: (36.1012°, 1.1995°)", |
| " el hed: (36.6500°, 4.7736°)", |
| " Grarem: (36.5161°, 6.3272°)", |
| " An Nāşirīyah: (32.6328°, 12.8736°)", |
| " Tolga: (34.7222°, 5.3784°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2830.08 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 274570.84 km²", |
| "FINAL ANSWER: Area: 274570.84 km², Perimeter: 2830.08 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 43.80486, |
| "lon": -79.35442, |
| "name": "Hillcrest Village" |
| }, |
| { |
| "lat": 42.55843, |
| "lon": -70.88005, |
| "name": "Beverly" |
| }, |
| { |
| "lat": 41.34621, |
| "lon": -73.079, |
| "name": "Ansonia" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 60853.35, |
| "perimeter_km": 1508.78, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Hillcrest Village: (43.8049°, -79.3544°)", |
| " Beverly: (42.5584°, -70.8800°)", |
| " Ansonia: (41.3462°, -73.0790°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 1508.78 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 60853.35 km²", |
| "FINAL ANSWER: Area: 60853.35 km², Perimeter: 1508.78 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 48.79266, |
| "lon": 2.46569, |
| "name": "Créteil" |
| }, |
| { |
| "lat": 57.76638, |
| "lon": 40.92828, |
| "name": "Kostroma" |
| }, |
| { |
| "lat": 44.62693, |
| "lon": 22.65288, |
| "name": "Drobeta-Turnu Severin" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1542652.66, |
| "perimeter_km": 6227.74, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Créteil: (48.7927°, 2.4657°)", |
| " Kostroma: (57.7664°, 40.9283°)", |
| " Drobeta-Turnu Severin: (44.6269°, 22.6529°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 6227.74 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1542652.66 km²", |
| "FINAL ANSWER: Area: 1542652.66 km², Perimeter: 6227.74 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 21.63333, |
| "lon": 108.95, |
| "name": "Xichang" |
| }, |
| { |
| "lat": 14.95472, |
| "lon": 120.89694, |
| "name": "Baliuag" |
| }, |
| { |
| "lat": 14.11356, |
| "lon": 121.55574, |
| "name": "Lucban" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 30199.19, |
| "perimeter_km": 3153.19, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Xichang: (21.6333°, 108.9500°)", |
| " Baliuag: (14.9547°, 120.8969°)", |
| " Lucban: (14.1136°, 121.5557°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3153.19 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 30199.19 km²", |
| "FINAL ANSWER: Area: 30199.19 km², Perimeter: 3153.19 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": -28.29389, |
| "lon": -49.93167, |
| "name": "São Joaquim" |
| }, |
| { |
| "lat": -23.20083, |
| "lon": -47.28694, |
| "name": "Salto" |
| }, |
| { |
| "lat": -14.52972, |
| "lon": -40.36528, |
| "name": "Poções" |
| }, |
| { |
| "lat": -12.53556, |
| "lon": -39.19083, |
| "name": "Cabaceiras do Paraguaçu" |
| }, |
| { |
| "lat": -8.87556, |
| "lon": -36.36667, |
| "name": "São João" |
| }, |
| { |
| "lat": -20.12861, |
| "lon": -40.30778, |
| "name": "Serra" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 549061.19, |
| "perimeter_km": 5251.98, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " São Joaquim: (-28.2939°, -49.9317°)", |
| " Salto: (-23.2008°, -47.2869°)", |
| " Poções: (-14.5297°, -40.3653°)", |
| " Cabaceiras do Paraguaçu: (-12.5356°, -39.1908°)", |
| " São João: (-8.8756°, -36.3667°)", |
| " Serra: (-20.1286°, -40.3078°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5251.98 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 549061.19 km²", |
| "FINAL ANSWER: Area: 549061.19 km², Perimeter: 5251.98 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": -34.5627, |
| "lon": -58.45829, |
| "name": "Belgrano" |
| }, |
| { |
| "lat": -25.44227, |
| "lon": -49.06795, |
| "name": "Piraquara" |
| }, |
| { |
| "lat": -14.06694, |
| "lon": -39.64056, |
| "name": "Ibirataia" |
| }, |
| { |
| "lat": -22.80389, |
| "lon": -43.37222, |
| "name": "São João de Meriti" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 402760.22, |
| "perimeter_km": 5972.17, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Belgrano: (-34.5627°, -58.4583°)", |
| " Piraquara: (-25.4423°, -49.0680°)", |
| " Ibirataia: (-14.0669°, -39.6406°)", |
| " São João de Meriti: (-22.8039°, -43.3722°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5972.17 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 402760.22 km²", |
| "FINAL ANSWER: Area: 402760.22 km², Perimeter: 5972.17 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 22.71667, |
| "lon": 70.28333, |
| "name": "Jodiya Bandar" |
| }, |
| { |
| "lat": 38.20835, |
| "lon": 67.20664, |
| "name": "Boysun" |
| }, |
| { |
| "lat": 40.35667, |
| "lon": 71.28472, |
| "name": "Rishton" |
| }, |
| { |
| "lat": 29.10298, |
| "lon": 75.17138, |
| "name": "Bhādra" |
| }, |
| { |
| "lat": 22.59573, |
| "lon": 76.9133, |
| "name": "Khātegaon" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1019201.97, |
| "perimeter_km": 4896.88, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Jodiya Bandar: (22.7167°, 70.2833°)", |
| " Boysun: (38.2084°, 67.2066°)", |
| " Rishton: (40.3567°, 71.2847°)", |
| " Bhādra: (29.1030°, 75.1714°)", |
| " Khātegaon: (22.5957°, 76.9133°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4896.88 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1019201.97 km²", |
| "FINAL ANSWER: Area: 1019201.97 km², Perimeter: 4896.88 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 34.80556, |
| "lon": 116.63889, |
| "name": "Shizhai" |
| }, |
| { |
| "lat": 35.47619, |
| "lon": 136.7721, |
| "name": "Yamagata" |
| }, |
| { |
| "lat": 32.94584, |
| "lon": 132.98635, |
| "name": "Shimoda" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 271586.21, |
| "perimeter_km": 3798.12, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Shizhai: (34.8056°, 116.6389°)", |
| " Yamagata: (35.4762°, 136.7721°)", |
| " Shimoda: (32.9458°, 132.9863°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3798.12 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 271586.21 km²", |
| "FINAL ANSWER: Area: 271586.21 km², Perimeter: 3798.12 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 19.59283, |
| "lon": -98.91084, |
| "name": "Tezoyuca" |
| }, |
| { |
| "lat": 29.77828, |
| "lon": -95.17188, |
| "name": "Cloverleaf" |
| }, |
| { |
| "lat": 27.29393, |
| "lon": -80.35033, |
| "name": "Port Saint Lucie" |
| }, |
| { |
| "lat": 14.30097, |
| "lon": -90.78816, |
| "name": "Escuintla" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1819230.45, |
| "perimeter_km": 5516.15, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Tezoyuca: (19.5928°, -98.9108°)", |
| " Cloverleaf: (29.7783°, -95.1719°)", |
| " Port Saint Lucie: (27.2939°, -80.3503°)", |
| " Escuintla: (14.3010°, -90.7882°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5516.15 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1819230.45 km²", |
| "FINAL ANSWER: Area: 1819230.45 km², Perimeter: 5516.15 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": -23.20554, |
| "lon": -46.7838, |
| "name": "Campo Limpo Paulista" |
| }, |
| { |
| "lat": -22.28306, |
| "lon": -46.36889, |
| "name": "Ouro Fino" |
| }, |
| { |
| "lat": -19.22, |
| "lon": -42.48361, |
| "name": "Belo Oriente" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 13840.0, |
| "perimeter_km": 1267.87, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Campo Limpo Paulista: (-23.2055°, -46.7838°)", |
| " Ouro Fino: (-22.2831°, -46.3689°)", |
| " Belo Oriente: (-19.2200°, -42.4836°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 1267.87 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 13840.00 km²", |
| "FINAL ANSWER: Area: 13840.00 km², Perimeter: 1267.87 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 19.02681, |
| "lon": 74.71487, |
| "name": "Ārangaon" |
| }, |
| { |
| "lat": 27.56155, |
| "lon": 73.47141, |
| "name": "Nokha" |
| }, |
| { |
| "lat": 31.80921, |
| "lon": 75.20294, |
| "name": "Batāla" |
| }, |
| { |
| "lat": 16.94761, |
| "lon": 81.77987, |
| "name": "Dowleswaram" |
| }, |
| { |
| "lat": 17.93023, |
| "lon": 80.82671, |
| "name": "Manuguru" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 680540.1, |
| "perimeter_km": 4043.9, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Ārangaon: (19.0268°, 74.7149°)", |
| " Nokha: (27.5616°, 73.4714°)", |
| " Batāla: (31.8092°, 75.2029°)", |
| " Dowleswaram: (16.9476°, 81.7799°)", |
| " Manuguru: (17.9302°, 80.8267°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4043.90 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 680540.10 km²", |
| "FINAL ANSWER: Area: 680540.10 km², Perimeter: 4043.90 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 17.52333, |
| "lon": 80.60405, |
| "name": "Chunchupally" |
| }, |
| { |
| "lat": 29.41223, |
| "lon": 76.9547, |
| "name": "Panipat Taraf Ansar" |
| }, |
| { |
| "lat": 26.71004, |
| "lon": 88.42851, |
| "name": "Siliguri" |
| }, |
| { |
| "lat": 16.10864, |
| "lon": 102.25808, |
| "name": "Kaeng Khro" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1918815.96, |
| "perimeter_km": 6698.61, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Chunchupally: (17.5233°, 80.6041°)", |
| " Panipat Taraf Ansar: (29.4122°, 76.9547°)", |
| " Siliguri: (26.7100°, 88.4285°)", |
| " Kaeng Khro: (16.1086°, 102.2581°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 6698.61 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1918815.96 km²", |
| "FINAL ANSWER: Area: 1918815.96 km², Perimeter: 6698.61 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 33.79833, |
| "lon": 117.86639, |
| "name": "Guanshan" |
| }, |
| { |
| "lat": 41.79556, |
| "lon": 129.77583, |
| "name": "Chongjin" |
| }, |
| { |
| "lat": 35.17325, |
| "lon": 137.05667, |
| "name": "Nagakute" |
| }, |
| { |
| "lat": 33.35634, |
| "lon": 130.74966, |
| "name": "Ukiha" |
| }, |
| { |
| "lat": 32.65, |
| "lon": 130.66667, |
| "name": "Matsubase" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 879823.55, |
| "perimeter_km": 4230.89, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Guanshan: (33.7983°, 117.8664°)", |
| " Chongjin: (41.7956°, 129.7758°)", |
| " Nagakute: (35.1733°, 137.0567°)", |
| " Ukiha: (33.3563°, 130.7497°)", |
| " Matsubase: (32.6500°, 130.6667°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4230.89 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 879823.55 km²", |
| "FINAL ANSWER: Area: 879823.55 km², Perimeter: 4230.89 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": -38.18333, |
| "lon": 145.08333, |
| "name": "Mount Eliza" |
| }, |
| { |
| "lat": -27.63917, |
| "lon": 153.10944, |
| "name": "Logan City" |
| }, |
| { |
| "lat": -28.11694, |
| "lon": 153.46584, |
| "name": "Palm Beach" |
| }, |
| { |
| "lat": -33.9125, |
| "lon": 151.10279, |
| "name": "Campsie" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 152287.19, |
| "perimeter_km": 2855.92, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Mount Eliza: (-38.1833°, 145.0833°)", |
| " Logan City: (-27.6392°, 153.1094°)", |
| " Palm Beach: (-28.1169°, 153.4658°)", |
| " Campsie: (-33.9125°, 151.1028°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2855.92 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 152287.19 km²", |
| "FINAL ANSWER: Area: 152287.19 km², Perimeter: 2855.92 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": -36.12179, |
| "lon": 146.88809, |
| "name": "Wodonga" |
| }, |
| { |
| "lat": -37.88333, |
| "lon": 145.21667, |
| "name": "Wantirna South" |
| }, |
| { |
| "lat": -38.08333, |
| "lon": 144.38333, |
| "name": "Corio" |
| }, |
| { |
| "lat": -26.65682, |
| "lon": 153.07955, |
| "name": "Sunshine Coast" |
| }, |
| { |
| "lat": -27.46794, |
| "lon": 153.02809, |
| "name": "Brisbane" |
| }, |
| { |
| "lat": -33.92598, |
| "lon": 151.19347, |
| "name": "Mascot" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 189299.75, |
| "perimeter_km": 3122.06, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Wodonga: (-36.1218°, 146.8881°)", |
| " Wantirna South: (-37.8833°, 145.2167°)", |
| " Corio: (-38.0833°, 144.3833°)", |
| " Sunshine Coast: (-26.6568°, 153.0796°)", |
| " Brisbane: (-27.4679°, 153.0281°)", |
| " Mascot: (-33.9260°, 151.1935°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3122.06 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 189299.75 km²", |
| "FINAL ANSWER: Area: 189299.75 km², Perimeter: 3122.06 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 52.2, |
| "lon": 0.11667, |
| "name": "Cambridge" |
| }, |
| { |
| "lat": 53.3618, |
| "lon": -2.73406, |
| "name": "Widnes" |
| }, |
| { |
| "lat": 46.21667, |
| "lon": 20.48333, |
| "name": "Makó" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 60868.09, |
| "perimeter_km": 3681.51, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Cambridge: (52.2000°, 0.1167°)", |
| " Widnes: (53.3618°, -2.7341°)", |
| " Makó: (46.2167°, 20.4833°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3681.51 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 60868.09 km²", |
| "FINAL ANSWER: Area: 60868.09 km², Perimeter: 3681.51 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": -37.76667, |
| "lon": 144.91667, |
| "name": "Moonee Ponds" |
| }, |
| { |
| "lat": -27.61025, |
| "lon": 153.05388, |
| "name": "Sunnybank Hills" |
| }, |
| { |
| "lat": -33.89743, |
| "lon": 150.93446, |
| "name": "Cabramatta" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 138343.13, |
| "perimeter_km": 2780.66, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Moonee Ponds: (-37.7667°, 144.9167°)", |
| " Sunnybank Hills: (-27.6103°, 153.0539°)", |
| " Cabramatta: (-33.8974°, 150.9345°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2780.66 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 138343.13 km²", |
| "FINAL ANSWER: Area: 138343.13 km², Perimeter: 2780.66 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": -31.70312, |
| "lon": 27.2329, |
| "name": "Lady Frere" |
| }, |
| { |
| "lat": -19.45, |
| "lon": 29.81667, |
| "name": "Gweru" |
| }, |
| { |
| "lat": -23.35, |
| "lon": 43.66667, |
| "name": "Toliara" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1031850.84, |
| "perimeter_km": 4748.44, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Lady Frere: (-31.7031°, 27.2329°)", |
| " Gweru: (-19.4500°, 29.8167°)", |
| " Toliara: (-23.3500°, 43.6667°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4748.44 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1031850.84 km²", |
| "FINAL ANSWER: Area: 1031850.84 km², Perimeter: 4748.44 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 12.01292, |
| "lon": -83.76449, |
| "name": "Bluefields" |
| }, |
| { |
| "lat": 15.86275, |
| "lon": -97.06835, |
| "name": "Puerto Escondido" |
| }, |
| { |
| "lat": 26.66729, |
| "lon": -81.88009, |
| "name": "North Fort Myers" |
| }, |
| { |
| "lat": 23.0072, |
| "lon": -82.4017, |
| "name": "Boyeros" |
| }, |
| { |
| "lat": 18.41538, |
| "lon": -70.03317, |
| "name": "Bajos de Haina" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 2049759.06, |
| "perimeter_km": 6903.5, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Bluefields: (12.0129°, -83.7645°)", |
| " Puerto Escondido: (15.8628°, -97.0683°)", |
| " North Fort Myers: (26.6673°, -81.8801°)", |
| " Boyeros: (23.0072°, -82.4017°)", |
| " Bajos de Haina: (18.4154°, -70.0332°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 6903.50 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 2049759.06 km²", |
| "FINAL ANSWER: Area: 2049759.06 km², Perimeter: 6903.50 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 35.87687, |
| "lon": 14.53592, |
| "name": "Żabbar" |
| }, |
| { |
| "lat": 44.77879, |
| "lon": 17.20629, |
| "name": "Banja Luka" |
| }, |
| { |
| "lat": 50.95843, |
| "lon": 13.93702, |
| "name": "Pirna" |
| }, |
| { |
| "lat": 49.77984, |
| "lon": 18.43688, |
| "name": "Havířov" |
| }, |
| { |
| "lat": 50.62036, |
| "lon": 26.23695, |
| "name": "Rivne" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 870553.06, |
| "perimeter_km": 4540.26, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Żabbar: (35.8769°, 14.5359°)", |
| " Banja Luka: (44.7788°, 17.2063°)", |
| " Pirna: (50.9584°, 13.9370°)", |
| " Havířov: (49.7798°, 18.4369°)", |
| " Rivne: (50.6204°, 26.2370°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4540.26 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 870553.06 km²", |
| "FINAL ANSWER: Area: 870553.06 km², Perimeter: 4540.26 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": -24.79889, |
| "lon": -53.30667, |
| "name": "Corbélia" |
| }, |
| { |
| "lat": -16.83056, |
| "lon": -49.53194, |
| "name": "Guapó" |
| }, |
| { |
| "lat": -15.67941, |
| "lon": -48.19667, |
| "name": "Brazlândia" |
| }, |
| { |
| "lat": -2.95528, |
| "lon": -44.80694, |
| "name": "São João Batista" |
| }, |
| { |
| "lat": -22.53722, |
| "lon": -42.98194, |
| "name": "Guapimirim" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1394988.28, |
| "perimeter_km": 5890.23, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Corbélia: (-24.7989°, -53.3067°)", |
| " Guapó: (-16.8306°, -49.5319°)", |
| " Brazlândia: (-15.6794°, -48.1967°)", |
| " São João Batista: (-2.9553°, -44.8069°)", |
| " Guapimirim: (-22.5372°, -42.9819°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5890.23 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1394988.28 km²", |
| "FINAL ANSWER: Area: 1394988.28 km², Perimeter: 5890.23 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": -33.79798, |
| "lon": 151.28826, |
| "name": "Manly" |
| }, |
| { |
| "lat": -38.19528, |
| "lon": 146.5415, |
| "name": "Traralgon" |
| }, |
| { |
| "lat": -37.99116, |
| "lon": 145.17385, |
| "name": "Keysborough" |
| }, |
| { |
| "lat": -31.09048, |
| "lon": 150.92905, |
| "name": "Tamworth" |
| }, |
| { |
| "lat": -28.00274, |
| "lon": 153.42999, |
| "name": "Surfers Paradise" |
| }, |
| { |
| "lat": -22.27407, |
| "lon": 166.44884, |
| "name": "Nouméa" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 545188.44, |
| "perimeter_km": 5536.49, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Manly: (-33.7980°, 151.2883°)", |
| " Traralgon: (-38.1953°, 146.5415°)", |
| " Keysborough: (-37.9912°, 145.1738°)", |
| " Tamworth: (-31.0905°, 150.9290°)", |
| " Surfers Paradise: (-28.0027°, 153.4300°)", |
| " Nouméa: (-22.2741°, 166.4488°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5536.49 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 545188.44 km²", |
| "FINAL ANSWER: Area: 545188.44 km², Perimeter: 5536.49 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": 4.9353, |
| "lon": -6.77828, |
| "name": "Watté" |
| }, |
| { |
| "lat": 10.86225, |
| "lon": 0.20762, |
| "name": "Dapaong" |
| }, |
| { |
| "lat": 12.55, |
| "lon": -0.96667, |
| "name": "Barogo" |
| }, |
| { |
| "lat": 14.3521, |
| "lon": 3.3168, |
| "name": "Filingué" |
| }, |
| { |
| "lat": 10.85009, |
| "lon": 8.199, |
| "name": "Dutsen Wai" |
| }, |
| { |
| "lat": 4.25671, |
| "lon": 18.41583, |
| "name": "Bimbo" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1705909.17, |
| "perimeter_km": 6538.57, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Watté: (4.9353°, -6.7783°)", |
| " Dapaong: (10.8622°, 0.2076°)", |
| " Barogo: (12.5500°, -0.9667°)", |
| " Filingué: (14.3521°, 3.3168°)", |
| " Dutsen Wai: (10.8501°, 8.1990°)", |
| " Bimbo: (4.2567°, 18.4158°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 6538.57 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1705909.17 km²", |
| "FINAL ANSWER: Area: 1705909.17 km², Perimeter: 6538.57 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 38.88247, |
| "lon": 16.60086, |
| "name": "Catanzaro" |
| }, |
| { |
| "lat": 55.93333, |
| "lon": 23.31667, |
| "name": "Šiauliai" |
| }, |
| { |
| "lat": 48.52496, |
| "lon": 25.03712, |
| "name": "Kolomyia" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 361087.67, |
| "perimeter_km": 4058.83, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Catanzaro: (38.8825°, 16.6009°)", |
| " Šiauliai: (55.9333°, 23.3167°)", |
| " Kolomyia: (48.5250°, 25.0371°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4058.83 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 361087.67 km²", |
| "FINAL ANSWER: Area: 361087.67 km², Perimeter: 4058.83 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 33.87029, |
| "lon": -117.92534, |
| "name": "Fullerton" |
| }, |
| { |
| "lat": 40.39162, |
| "lon": -111.85077, |
| "name": "Lehi" |
| }, |
| { |
| "lat": 37.7528, |
| "lon": -100.01708, |
| "name": "Dodge City" |
| }, |
| { |
| "lat": 33.10317, |
| "lon": -96.67055, |
| "name": "Allen" |
| }, |
| { |
| "lat": 31.08351, |
| "lon": -97.65974, |
| "name": "Harker Heights" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1134620.66, |
| "perimeter_km": 4729.86, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Fullerton: (33.8703°, -117.9253°)", |
| " Lehi: (40.3916°, -111.8508°)", |
| " Dodge City: (37.7528°, -100.0171°)", |
| " Allen: (33.1032°, -96.6706°)", |
| " Harker Heights: (31.0835°, -97.6597°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4729.86 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1134620.66 km²", |
| "FINAL ANSWER: Area: 1134620.66 km², Perimeter: 4729.86 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": -20.95361, |
| "lon": -43.80639, |
| "name": "Carandaí" |
| }, |
| { |
| "lat": -23.68611, |
| "lon": -46.62278, |
| "name": "Diadema" |
| }, |
| { |
| "lat": -10.685, |
| "lon": -37.42528, |
| "name": "Itabaiana" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 55098.38, |
| "perimeter_km": 3492.83, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Carandaí: (-20.9536°, -43.8064°)", |
| " Diadema: (-23.6861°, -46.6228°)", |
| " Itabaiana: (-10.6850°, -37.4253°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3492.83 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 55098.38 km²", |
| "FINAL ANSWER: Area: 55098.38 km², Perimeter: 3492.83 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": -41.33333, |
| "lon": 173.18333, |
| "name": "Richmond" |
| }, |
| { |
| "lat": -39.06667, |
| "lon": 174.08333, |
| "name": "New Plymouth" |
| }, |
| { |
| "lat": -36.84103, |
| "lon": 174.65223, |
| "name": "Te Atatu Peninsula" |
| }, |
| { |
| "lat": -39.4926, |
| "lon": 176.91233, |
| "name": "Napier" |
| }, |
| { |
| "lat": -41.13333, |
| "lon": 174.85, |
| "name": "Porirua" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 80162.08, |
| "perimeter_km": 1264.54, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Richmond: (-41.3333°, 173.1833°)", |
| " New Plymouth: (-39.0667°, 174.0833°)", |
| " Te Atatu Peninsula: (-36.8410°, 174.6522°)", |
| " Napier: (-39.4926°, 176.9123°)", |
| " Porirua: (-41.1333°, 174.8500°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 1264.54 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 80162.08 km²", |
| "FINAL ANSWER: Area: 80162.08 km², Perimeter: 1264.54 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": -35.02692, |
| "lon": 117.88369, |
| "name": "Albany" |
| }, |
| { |
| "lat": -33.2792, |
| "lon": 115.71504, |
| "name": "Australind" |
| }, |
| { |
| "lat": -32.5269, |
| "lon": 115.7217, |
| "name": "Mandurah" |
| }, |
| { |
| "lat": -31.89578, |
| "lon": 115.76431, |
| "name": "Scarborough" |
| }, |
| { |
| "lat": -34.92866, |
| "lon": 138.59863, |
| "name": "Adelaide" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 324848.49, |
| "perimeter_km": 4457.73, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Albany: (-35.0269°, 117.8837°)", |
| " Australind: (-33.2792°, 115.7150°)", |
| " Mandurah: (-32.5269°, 115.7217°)", |
| " Scarborough: (-31.8958°, 115.7643°)", |
| " Adelaide: (-34.9287°, 138.5986°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4457.73 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 324848.49 km²", |
| "FINAL ANSWER: Area: 324848.49 km², Perimeter: 4457.73 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": -37.87709, |
| "lon": 145.12939, |
| "name": "Mount Waverley" |
| }, |
| { |
| "lat": -33.41665, |
| "lon": 149.5806, |
| "name": "Bathurst" |
| }, |
| { |
| "lat": -33.85, |
| "lon": 151.03333, |
| "name": "Auburn" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 43500.13, |
| "perimeter_km": 1476.36, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Mount Waverley: (-37.8771°, 145.1294°)", |
| " Bathurst: (-33.4166°, 149.5806°)", |
| " Auburn: (-33.8500°, 151.0333°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 1476.36 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 43500.13 km²", |
| "FINAL ANSWER: Area: 43500.13 km², Perimeter: 1476.36 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": 34.05529, |
| "lon": -117.75228, |
| "name": "Pomona" |
| }, |
| { |
| "lat": 34.26945, |
| "lon": -118.78148, |
| "name": "Simi Valley" |
| }, |
| { |
| "lat": 44.98595, |
| "lon": -122.98287, |
| "name": "Hayesville" |
| }, |
| { |
| "lat": 47.78815, |
| "lon": -122.30874, |
| "name": "Mountlake Terrace" |
| }, |
| { |
| "lat": 32.95373, |
| "lon": -96.89028, |
| "name": "Carrollton" |
| }, |
| { |
| "lat": 32.75957, |
| "lon": -97.45835, |
| "name": "White Settlement" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1710297.36, |
| "perimeter_km": 6292.53, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Pomona: (34.0553°, -117.7523°)", |
| " Simi Valley: (34.2694°, -118.7815°)", |
| " Hayesville: (44.9860°, -122.9829°)", |
| " Mountlake Terrace: (47.7882°, -122.3087°)", |
| " Carrollton: (32.9537°, -96.8903°)", |
| " White Settlement: (32.7596°, -97.4583°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 6292.53 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1710297.36 km²", |
| "FINAL ANSWER: Area: 1710297.36 km², Perimeter: 6292.53 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 16.07, |
| "lon": 120.4025, |
| "name": "Mangaldan" |
| }, |
| { |
| "lat": 14.2973, |
| "lon": 121.4598, |
| "name": "Lumbang" |
| }, |
| { |
| "lat": 6.89814, |
| "lon": 126.00961, |
| "name": "Lupon" |
| }, |
| { |
| "lat": 7.73028, |
| "lon": 125.09889, |
| "name": "Quezon" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 27076.54, |
| "perimeter_km": 2383.71, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Mangaldan: (16.0700°, 120.4025°)", |
| " Lumbang: (14.2973°, 121.4598°)", |
| " Lupon: (6.8981°, 126.0096°)", |
| " Quezon: (7.7303°, 125.0989°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2383.71 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 27076.54 km²", |
| "FINAL ANSWER: Area: 27076.54 km², Perimeter: 2383.71 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": -37.73333, |
| "lon": 145.15, |
| "name": "Eltham" |
| }, |
| { |
| "lat": -37.8318, |
| "lon": 140.77919, |
| "name": "Mount Gambier" |
| }, |
| { |
| "lat": -27.49325, |
| "lon": 153.05826, |
| "name": "Coorparoo" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 206040.72, |
| "perimeter_km": 3364.06, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Eltham: (-37.7333°, 145.1500°)", |
| " Mount Gambier: (-37.8318°, 140.7792°)", |
| " Coorparoo: (-27.4932°, 153.0583°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3364.06 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 206040.72 km²", |
| "FINAL ANSWER: Area: 206040.72 km², Perimeter: 3364.06 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 25.98454, |
| "lon": -80.19894, |
| "name": "West Park" |
| }, |
| { |
| "lat": 41.4156, |
| "lon": -81.92347, |
| "name": "North Olmsted" |
| }, |
| { |
| "lat": 46.05007, |
| "lon": -71.96579, |
| "name": "Victoriaville" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 716064.43, |
| "perimeter_km": 5021.4, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " West Park: (25.9845°, -80.1989°)", |
| " North Olmsted: (41.4156°, -81.9235°)", |
| " Victoriaville: (46.0501°, -71.9658°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5021.40 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 716064.43 km²", |
| "FINAL ANSWER: Area: 716064.43 km², Perimeter: 5021.40 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 13.2954, |
| "lon": 19.6966, |
| "name": "Umm Hājar" |
| }, |
| { |
| "lat": 2.46335, |
| "lon": 31.49832, |
| "name": "Pakwach" |
| }, |
| { |
| "lat": -3.28333, |
| "lon": 32.85, |
| "name": "Mhango" |
| }, |
| { |
| "lat": -8.3, |
| "lon": 31.51667, |
| "name": "Matai" |
| }, |
| { |
| "lat": -1.8628, |
| "lon": 29.62541, |
| "name": "Ngororero" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1087862.78, |
| "perimeter_km": 5759.88, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Umm Hājar: (13.2954°, 19.6966°)", |
| " Pakwach: (2.4634°, 31.4983°)", |
| " Mhango: (-3.2833°, 32.8500°)", |
| " Matai: (-8.3000°, 31.5167°)", |
| " Ngororero: (-1.8628°, 29.6254°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5759.88 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1087862.78 km²", |
| "FINAL ANSWER: Area: 1087862.78 km², Perimeter: 5759.88 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 16.25624, |
| "lon": 97.7246, |
| "name": "Mudon" |
| }, |
| { |
| "lat": 31.16611, |
| "lon": 112.58306, |
| "name": "Zhongxiang" |
| }, |
| { |
| "lat": 36.22107, |
| "lon": 118.69663, |
| "name": "Yishan" |
| }, |
| { |
| "lat": 23.73333, |
| "lon": 114.68333, |
| "name": "Heyuan" |
| }, |
| { |
| "lat": 14.96806, |
| "lon": 120.95472, |
| "name": "Pantubig" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 2325345.79, |
| "perimeter_km": 8143.29, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Mudon: (16.2562°, 97.7246°)", |
| " Zhongxiang: (31.1661°, 112.5831°)", |
| " Yishan: (36.2211°, 118.6966°)", |
| " Heyuan: (23.7333°, 114.6833°)", |
| " Pantubig: (14.9681°, 120.9547°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 8143.29 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 2325345.79 km²", |
| "FINAL ANSWER: Area: 2325345.79 km², Perimeter: 8143.29 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 51.28635, |
| "lon": 7.29388, |
| "name": "Schwelm" |
| }, |
| { |
| "lat": 52.57601, |
| "lon": 13.29389, |
| "name": "Tegel" |
| }, |
| { |
| "lat": 55.01457, |
| "lon": 36.47185, |
| "name": "Maloyaroslavets" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 14889.3, |
| "perimeter_km": 3948.38, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Schwelm: (51.2863°, 7.2939°)", |
| " Tegel: (52.5760°, 13.2939°)", |
| " Maloyaroslavets: (55.0146°, 36.4719°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3948.38 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 14889.30 km²", |
| "FINAL ANSWER: Area: 14889.30 km², Perimeter: 3948.38 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": 38.06147, |
| "lon": -1.04877, |
| "name": "Santomera" |
| }, |
| { |
| "lat": 42.64725, |
| "lon": -8.88459, |
| "name": "Boiro" |
| }, |
| { |
| "lat": 53.57077, |
| "lon": -1.18454, |
| "name": "Adwick le Street" |
| }, |
| { |
| "lat": 49.34615, |
| "lon": 7.25527, |
| "name": "Bexbach" |
| }, |
| { |
| "lat": 48.2019, |
| "lon": 16.38792, |
| "name": "Landstraße" |
| }, |
| { |
| "lat": 44.16259, |
| "lon": 4.61974, |
| "name": "Bagnols-sur-Cèze" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1683739.72, |
| "perimeter_km": 5444.59, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Santomera: (38.0615°, -1.0488°)", |
| " Boiro: (42.6472°, -8.8846°)", |
| " Adwick le Street: (53.5708°, -1.1845°)", |
| " Bexbach: (49.3462°, 7.2553°)", |
| " Landstraße: (48.2019°, 16.3879°)", |
| " Bagnols-sur-Cèze: (44.1626°, 4.6197°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5444.59 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1683739.72 km²", |
| "FINAL ANSWER: Area: 1683739.72 km², Perimeter: 5444.59 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 6.67342, |
| "lon": -3.96938, |
| "name": "Arrah" |
| }, |
| { |
| "lat": 10.28333, |
| "lon": -4.91667, |
| "name": "Niangoloko" |
| }, |
| { |
| "lat": 12.87695, |
| "lon": 10.45536, |
| "name": "Nguru" |
| }, |
| { |
| "lat": 9.87342, |
| "lon": 7.95407, |
| "name": "Kachia" |
| }, |
| { |
| "lat": 7.25256, |
| "lon": 5.19312, |
| "name": "Akure" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 670685.25, |
| "perimeter_km": 3978.75, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Arrah: (6.6734°, -3.9694°)", |
| " Niangoloko: (10.2833°, -4.9167°)", |
| " Nguru: (12.8770°, 10.4554°)", |
| " Kachia: (9.8734°, 7.9541°)", |
| " Akure: (7.2526°, 5.1931°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3978.75 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 670685.25 km²", |
| "FINAL ANSWER: Area: 670685.25 km², Perimeter: 3978.75 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 24.69285, |
| "lon": 108.08376, |
| "name": "Hechi" |
| }, |
| { |
| "lat": 30.01651, |
| "lon": 105.7973, |
| "name": "Tangba" |
| }, |
| { |
| "lat": 30.08333, |
| "lon": 114.95, |
| "name": "Daye" |
| }, |
| { |
| "lat": 28.8547, |
| "lon": 120.73168, |
| "name": "Xianju" |
| }, |
| { |
| "lat": 22.99376, |
| "lon": 114.71311, |
| "name": "Pingshan" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 755014.43, |
| "perimeter_km": 3677.22, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Hechi: (24.6928°, 108.0838°)", |
| " Tangba: (30.0165°, 105.7973°)", |
| " Daye: (30.0833°, 114.9500°)", |
| " Xianju: (28.8547°, 120.7317°)", |
| " Pingshan: (22.9938°, 114.7131°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3677.22 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 755014.43 km²", |
| "FINAL ANSWER: Area: 755014.43 km², Perimeter: 3677.22 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": 50.77926, |
| "lon": 4.24355, |
| "name": "Sint-Pieters-Leeuw" |
| }, |
| { |
| "lat": 50.54581, |
| "lon": -3.49671, |
| "name": "Teignmouth" |
| }, |
| { |
| "lat": 51.52279, |
| "lon": -0.71986, |
| "name": "Maidenhead" |
| }, |
| { |
| "lat": 53.63301, |
| "lon": 9.83945, |
| "name": "Halstenbek" |
| }, |
| { |
| "lat": 50.90383, |
| "lon": 7.40306, |
| "name": "Much" |
| }, |
| { |
| "lat": 47.6895, |
| "lon": 9.83247, |
| "name": "Wangen" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 173111.91, |
| "perimeter_km": 2794.29, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Sint-Pieters-Leeuw: (50.7793°, 4.2435°)", |
| " Teignmouth: (50.5458°, -3.4967°)", |
| " Maidenhead: (51.5228°, -0.7199°)", |
| " Halstenbek: (53.6330°, 9.8394°)", |
| " Much: (50.9038°, 7.4031°)", |
| " Wangen: (47.6895°, 9.8325°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2794.29 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 173111.91 km²", |
| "FINAL ANSWER: Area: 173111.91 km², Perimeter: 2794.29 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": -23.55083, |
| "lon": -51.46083, |
| "name": "Apucarana" |
| }, |
| { |
| "lat": -12.54528, |
| "lon": -55.71139, |
| "name": "Sorriso" |
| }, |
| { |
| "lat": -15.47949, |
| "lon": -44.3652, |
| "name": "Januária" |
| }, |
| { |
| "lat": -19.31111, |
| "lon": -46.04889, |
| "name": "São Gotardo" |
| }, |
| { |
| "lat": -20.99139, |
| "lon": -47.65861, |
| "name": "Brodowski" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 755889.04, |
| "perimeter_km": 3766.93, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Apucarana: (-23.5508°, -51.4608°)", |
| " Sorriso: (-12.5453°, -55.7114°)", |
| " Januária: (-15.4795°, -44.3652°)", |
| " São Gotardo: (-19.3111°, -46.0489°)", |
| " Brodowski: (-20.9914°, -47.6586°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3766.93 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 755889.04 km²", |
| "FINAL ANSWER: Area: 755889.04 km², Perimeter: 3766.93 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": 37.61915, |
| "lon": -0.87799, |
| "name": "La Unión" |
| }, |
| { |
| "lat": 49.46307, |
| "lon": 1.09364, |
| "name": "Mont-Saint-Aignan" |
| }, |
| { |
| "lat": 51.61379, |
| "lon": 7.19738, |
| "name": "Recklinghausen" |
| }, |
| { |
| "lat": 54.23575, |
| "lon": 10.27934, |
| "name": "Preetz" |
| }, |
| { |
| "lat": 49.94782, |
| "lon": 11.57893, |
| "name": "Bayreuth" |
| }, |
| { |
| "lat": 41.99771, |
| "lon": 12.61814, |
| "name": "Tor Lupara" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1165381.42, |
| "perimeter_km": 4798.86, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " La Unión: (37.6191°, -0.8780°)", |
| " Mont-Saint-Aignan: (49.4631°, 1.0936°)", |
| " Recklinghausen: (51.6138°, 7.1974°)", |
| " Preetz: (54.2358°, 10.2793°)", |
| " Bayreuth: (49.9478°, 11.5789°)", |
| " Tor Lupara: (41.9977°, 12.6181°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4798.86 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1165381.42 km²", |
| "FINAL ANSWER: Area: 1165381.42 km², Perimeter: 4798.86 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 41.42861, |
| "lon": 2.1741, |
| "name": "Vilapicina i la Torre Llobeta" |
| }, |
| { |
| "lat": 42.81483, |
| "lon": -1.64898, |
| "name": "Primer Ensanche" |
| }, |
| { |
| "lat": 48.77935, |
| "lon": 2.33729, |
| "name": "L'Haÿ-les-Roses" |
| }, |
| { |
| "lat": 51.7575, |
| "lon": 4.16528, |
| "name": "Middelharnis" |
| }, |
| { |
| "lat": 51.71905, |
| "lon": 8.75439, |
| "name": "Paderborn" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 359027.83, |
| "perimeter_km": 3002.7, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Vilapicina i la Torre Llobeta: (41.4286°, 2.1741°)", |
| " Primer Ensanche: (42.8148°, -1.6490°)", |
| " L'Haÿ-les-Roses: (48.7794°, 2.3373°)", |
| " Middelharnis: (51.7575°, 4.1653°)", |
| " Paderborn: (51.7191°, 8.7544°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3002.70 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 359027.83 km²", |
| "FINAL ANSWER: Area: 359027.83 km², Perimeter: 3002.70 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 34.73564, |
| "lon": 105.32632, |
| "name": "Gangu Chengguanzhen" |
| }, |
| { |
| "lat": 44.67024, |
| "lon": 102.17491, |
| "name": "Bogd" |
| }, |
| { |
| "lat": 33.25333, |
| "lon": 126.56181, |
| "name": "Seogwipo" |
| }, |
| { |
| "lat": 22.36718, |
| "lon": 114.12347, |
| "name": "Tai Wo Hau" |
| }, |
| { |
| "lat": 23.17233, |
| "lon": 112.28298, |
| "name": "Lubu" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 2538190.62, |
| "perimeter_km": 6962.75, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Gangu Chengguanzhen: (34.7356°, 105.3263°)", |
| " Bogd: (44.6702°, 102.1749°)", |
| " Seogwipo: (33.2533°, 126.5618°)", |
| " Tai Wo Hau: (22.3672°, 114.1235°)", |
| " Lubu: (23.1723°, 112.2830°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 6962.75 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 2538190.62 km²", |
| "FINAL ANSWER: Area: 2538190.62 km², Perimeter: 6962.75 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 37.22661, |
| "lon": -121.97468, |
| "name": "Los Gatos" |
| }, |
| { |
| "lat": 47.78815, |
| "lon": -122.30874, |
| "name": "Mountlake Terrace" |
| }, |
| { |
| "lat": 37.67748, |
| "lon": -113.06189, |
| "name": "Cedar City" |
| }, |
| { |
| "lat": 33.46697, |
| "lon": -117.69811, |
| "name": "Dana Point" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 640325.18, |
| "perimeter_km": 3725.39, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Los Gatos: (37.2266°, -121.9747°)", |
| " Mountlake Terrace: (47.7882°, -122.3087°)", |
| " Cedar City: (37.6775°, -113.0619°)", |
| " Dana Point: (33.4670°, -117.6981°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3725.39 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 640325.18 km²", |
| "FINAL ANSWER: Area: 640325.18 km², Perimeter: 3725.39 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 34.68473, |
| "lon": -6.00344, |
| "name": "Souk El Arbaa" |
| }, |
| { |
| "lat": 35.07465, |
| "lon": -1.22431, |
| "name": "Bensekrane" |
| }, |
| { |
| "lat": 35.65903, |
| "lon": -0.52168, |
| "name": "Sidi ech Chahmi" |
| }, |
| { |
| "lat": 36.4, |
| "lon": 10.61667, |
| "name": "Hammamet" |
| }, |
| { |
| "lat": 31.09755, |
| "lon": 31.30312, |
| "name": "Nabarūh" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 388965.52, |
| "perimeter_km": 7016.55, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Souk El Arbaa: (34.6847°, -6.0034°)", |
| " Bensekrane: (35.0746°, -1.2243°)", |
| " Sidi ech Chahmi: (35.6590°, -0.5217°)", |
| " Hammamet: (36.4000°, 10.6167°)", |
| " Nabarūh: (31.0975°, 31.3031°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 7016.55 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 388965.52 km²", |
| "FINAL ANSWER: Area: 388965.52 km², Perimeter: 7016.55 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 53.59245, |
| "lon": -2.21941, |
| "name": "Heywood" |
| }, |
| { |
| "lat": 53.56321, |
| "lon": 9.94257, |
| "name": "Altona-Nord" |
| }, |
| { |
| "lat": 45.76873, |
| "lon": 4.95883, |
| "name": "Décines-Charpieu" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 355362.27, |
| "perimeter_km": 2749.93, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Heywood: (53.5924°, -2.2194°)", |
| " Altona-Nord: (53.5632°, 9.9426°)", |
| " Décines-Charpieu: (45.7687°, 4.9588°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2749.93 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 355362.27 km²", |
| "FINAL ANSWER: Area: 355362.27 km², Perimeter: 2749.93 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 50.13423, |
| "lon": 8.91418, |
| "name": "Hanau am Main" |
| }, |
| { |
| "lat": 50.55162, |
| "lon": 9.67518, |
| "name": "Fulda" |
| }, |
| { |
| "lat": 45.83111, |
| "lon": 16.11639, |
| "name": "Sesvete" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 25198.41, |
| "perimeter_km": 1498.21, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Hanau am Main: (50.1342°, 8.9142°)", |
| " Fulda: (50.5516°, 9.6752°)", |
| " Sesvete: (45.8311°, 16.1164°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 1498.21 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 25198.41 km²", |
| "FINAL ANSWER: Area: 25198.41 km², Perimeter: 1498.21 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": -15.77972, |
| "lon": -47.92972, |
| "name": "Brasília" |
| }, |
| { |
| "lat": -11.86417, |
| "lon": -55.5025, |
| "name": "Sinop" |
| }, |
| { |
| "lat": -11.51917, |
| "lon": -37.51167, |
| "name": "Indiaroba" |
| }, |
| { |
| "lat": -13.4425, |
| "lon": -42.23889, |
| "name": "Paramirim" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 433452.52, |
| "perimeter_km": 4106.29, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Brasília: (-15.7797°, -47.9297°)", |
| " Sinop: (-11.8642°, -55.5025°)", |
| " Indiaroba: (-11.5192°, -37.5117°)", |
| " Paramirim: (-13.4425°, -42.2389°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4106.29 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 433452.52 km²", |
| "FINAL ANSWER: Area: 433452.52 km², Perimeter: 4106.29 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 30.52297, |
| "lon": -87.90333, |
| "name": "Fairhope" |
| }, |
| { |
| "lat": 35.75647, |
| "lon": -83.97046, |
| "name": "Maryville" |
| }, |
| { |
| "lat": 43.04812, |
| "lon": -76.14742, |
| "name": "Syracuse" |
| }, |
| { |
| "lat": 40.08927, |
| "lon": -75.39602, |
| "name": "King of Prussia" |
| }, |
| { |
| "lat": 22.49502, |
| "lon": -79.54548, |
| "name": "Remedios" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1208249.87, |
| "perimeter_km": 5288.65, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Fairhope: (30.5230°, -87.9033°)", |
| " Maryville: (35.7565°, -83.9705°)", |
| " Syracuse: (43.0481°, -76.1474°)", |
| " King of Prussia: (40.0893°, -75.3960°)", |
| " Remedios: (22.4950°, -79.5455°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5288.65 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1208249.87 km²", |
| "FINAL ANSWER: Area: 1208249.87 km², Perimeter: 5288.65 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 34.92915, |
| "lon": 43.48878, |
| "name": "Bayjī" |
| }, |
| { |
| "lat": 37.45517, |
| "lon": 35.81573, |
| "name": "Kozan" |
| }, |
| { |
| "lat": 36.90124, |
| "lon": 54.07195, |
| "name": "Bandar-e Torkaman" |
| }, |
| { |
| "lat": 32.59702, |
| "lon": 74.14652, |
| "name": "Sook Kalan" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 536981.48, |
| "perimeter_km": 7085.75, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Bayjī: (34.9291°, 43.4888°)", |
| " Kozan: (37.4552°, 35.8157°)", |
| " Bandar-e Torkaman: (36.9012°, 54.0720°)", |
| " Sook Kalan: (32.5970°, 74.1465°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 7085.75 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 536981.48 km²", |
| "FINAL ANSWER: Area: 536981.48 km², Perimeter: 7085.75 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": 37.40881, |
| "lon": -4.48522, |
| "name": "Lucena" |
| }, |
| { |
| "lat": 42.82562, |
| "lon": -1.61671, |
| "name": "Burlata" |
| }, |
| { |
| "lat": 54.95, |
| "lon": -7.73333, |
| "name": "Letterkenny" |
| }, |
| { |
| "lat": 51.12637, |
| "lon": 15.91979, |
| "name": "Złotoryja" |
| }, |
| { |
| "lat": 48.89452, |
| "lon": 18.04436, |
| "name": "Trenčín" |
| }, |
| { |
| "lat": 36.9084, |
| "lon": 15.13937, |
| "name": "Avola" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 3373023.77, |
| "perimeter_km": 7078.77, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Lucena: (37.4088°, -4.4852°)", |
| " Burlata: (42.8256°, -1.6167°)", |
| " Letterkenny: (54.9500°, -7.7333°)", |
| " Złotoryja: (51.1264°, 15.9198°)", |
| " Trenčín: (48.8945°, 18.0444°)", |
| " Avola: (36.9084°, 15.1394°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 7078.77 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 3373023.77 km²", |
| "FINAL ANSWER: Area: 3373023.77 km², Perimeter: 7078.77 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 42.78752, |
| "lon": -86.10893, |
| "name": "Holland" |
| }, |
| { |
| "lat": 42.95947, |
| "lon": -85.48975, |
| "name": "Forest Hills" |
| }, |
| { |
| "lat": 40.58867, |
| "lon": -83.12852, |
| "name": "Marion" |
| }, |
| { |
| "lat": 27.71809, |
| "lon": -82.35176, |
| "name": "Sun City Center" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 174019.77, |
| "perimeter_km": 3524.75, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Holland: (42.7875°, -86.1089°)", |
| " Forest Hills: (42.9595°, -85.4898°)", |
| " Marion: (40.5887°, -83.1285°)", |
| " Sun City Center: (27.7181°, -82.3518°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3524.75 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 174019.77 km²", |
| "FINAL ANSWER: Area: 174019.77 km², Perimeter: 3524.75 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": -19.05294, |
| "lon": -169.91957, |
| "name": "Alofi" |
| }, |
| { |
| "lat": -13.83333, |
| "lon": -171.76666, |
| "name": "Apia" |
| }, |
| { |
| "lat": -13.28163, |
| "lon": -176.17453, |
| "name": "Mata-Utu" |
| }, |
| { |
| "lat": -18.11094, |
| "lon": 178.40943, |
| "name": "Lami" |
| }, |
| { |
| "lat": -18.14307, |
| "lon": 177.50691, |
| "name": "Sigatoka" |
| }, |
| { |
| "lat": -29.05459, |
| "lon": 167.96628, |
| "name": "Kingston" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1411739.62, |
| "perimeter_km": 6031.55, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Alofi: (-19.0529°, -169.9196°)", |
| " Apia: (-13.8333°, -171.7667°)", |
| " Mata-Utu: (-13.2816°, -176.1745°)", |
| " Lami: (-18.1109°, 178.4094°)", |
| " Sigatoka: (-18.1431°, 177.5069°)", |
| " Kingston: (-29.0546°, 167.9663°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 6031.55 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1411739.62 km²", |
| "FINAL ANSWER: Area: 1411739.62 km², Perimeter: 6031.55 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 25.85587, |
| "lon": 88.35943, |
| "name": "Pīrgaaj" |
| }, |
| { |
| "lat": 32.44201, |
| "lon": 105.823, |
| "name": "Guangyuan" |
| }, |
| { |
| "lat": 14.5832, |
| "lon": 121.0409, |
| "name": "Mandaluyong City" |
| }, |
| { |
| "lat": 21.05, |
| "lon": 105.8, |
| "name": "Nghĩa Đô" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 2252179.61, |
| "perimeter_km": 7978.55, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Pīrgaaj: (25.8559°, 88.3594°)", |
| " Guangyuan: (32.4420°, 105.8230°)", |
| " Mandaluyong City: (14.5832°, 121.0409°)", |
| " Nghĩa Đô: (21.0500°, 105.8000°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 7978.55 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 2252179.61 km²", |
| "FINAL ANSWER: Area: 2252179.61 km², Perimeter: 7978.55 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 31.86541, |
| "lon": 73.50875, |
| "name": "Sukheke Mandi" |
| }, |
| { |
| "lat": 41.25832, |
| "lon": 67.96991, |
| "name": "Shardara" |
| }, |
| { |
| "lat": 27.14872, |
| "lon": 79.50078, |
| "name": "Chhibrāmau" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 197182.1, |
| "perimeter_km": 3826.35, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Sukheke Mandi: (31.8654°, 73.5088°)", |
| " Shardara: (41.2583°, 67.9699°)", |
| " Chhibrāmau: (27.1487°, 79.5008°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3826.35 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 197182.10 km²", |
| "FINAL ANSWER: Area: 197182.10 km², Perimeter: 3826.35 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": -37.70988, |
| "lon": 144.75483, |
| "name": "Taylors Hill" |
| }, |
| { |
| "lat": -37.56622, |
| "lon": 143.84957, |
| "name": "Ballarat" |
| }, |
| { |
| "lat": -33.41665, |
| "lon": 149.5806, |
| "name": "Bathurst" |
| }, |
| { |
| "lat": -32.83211, |
| "lon": 151.35623, |
| "name": "Cessnock" |
| }, |
| { |
| "lat": -33.79176, |
| "lon": 151.08057, |
| "name": "Eastwood" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 72978.34, |
| "perimeter_km": 1780.58, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Taylors Hill: (-37.7099°, 144.7548°)", |
| " Ballarat: (-37.5662°, 143.8496°)", |
| " Bathurst: (-33.4166°, 149.5806°)", |
| " Cessnock: (-32.8321°, 151.3562°)", |
| " Eastwood: (-33.7918°, 151.0806°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 1780.58 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 72978.34 km²", |
| "FINAL ANSWER: Area: 72978.34 km², Perimeter: 1780.58 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": -23.56786, |
| "lon": -46.54599, |
| "name": "Vila Formosa" |
| }, |
| { |
| "lat": -13.65145, |
| "lon": -41.84564, |
| "name": "Livramento do Brumado" |
| }, |
| { |
| "lat": -12.13556, |
| "lon": -38.41917, |
| "name": "Alagoinhas" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 167429.29, |
| "perimeter_km": 3150.09, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Vila Formosa: (-23.5679°, -46.5460°)", |
| " Livramento do Brumado: (-13.6515°, -41.8456°)", |
| " Alagoinhas: (-12.1356°, -38.4192°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3150.09 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 167429.29 km²", |
| "FINAL ANSWER: Area: 167429.29 km², Perimeter: 3150.09 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": 34.60593, |
| "lon": -86.98334, |
| "name": "Decatur" |
| }, |
| { |
| "lat": 35.61507, |
| "lon": -87.03528, |
| "name": "Columbia" |
| }, |
| { |
| "lat": 42.00864, |
| "lon": -87.66672, |
| "name": "Rogers Park" |
| }, |
| { |
| "lat": 40.3634, |
| "lon": -79.86644, |
| "name": "West Mifflin" |
| }, |
| { |
| "lat": 40.72316, |
| "lon": -73.91264, |
| "name": "Maspeth" |
| }, |
| { |
| "lat": 40.72982, |
| "lon": -73.21039, |
| "name": "Islip" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 421671.93, |
| "perimeter_km": 3454.78, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Decatur: (34.6059°, -86.9833°)", |
| " Columbia: (35.6151°, -87.0353°)", |
| " Rogers Park: (42.0086°, -87.6667°)", |
| " West Mifflin: (40.3634°, -79.8664°)", |
| " Maspeth: (40.7232°, -73.9126°)", |
| " Islip: (40.7298°, -73.2104°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3454.78 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 421671.93 km²", |
| "FINAL ANSWER: Area: 421671.93 km², Perimeter: 3454.78 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": -7.41667, |
| "lon": 30.6, |
| "name": "Kirando" |
| }, |
| { |
| "lat": -1.9275, |
| "lon": 18.2881, |
| "name": "Inongo" |
| }, |
| { |
| "lat": 14.10776, |
| "lon": 34.09197, |
| "name": "Al-Fāw" |
| }, |
| { |
| "lat": 14.88722, |
| "lon": 38.81528, |
| "name": "Mendefera" |
| }, |
| { |
| "lat": 0.64996, |
| "lon": 33.17128, |
| "name": "Buwenge" |
| }, |
| { |
| "lat": 0.43333, |
| "lon": 31.23333, |
| "name": "Kasambya" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 2515674.62, |
| "perimeter_km": 7295.16, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Kirando: (-7.4167°, 30.6000°)", |
| " Inongo: (-1.9275°, 18.2881°)", |
| " Al-Fāw: (14.1078°, 34.0920°)", |
| " Mendefera: (14.8872°, 38.8153°)", |
| " Buwenge: (0.6500°, 33.1713°)", |
| " Kasambya: (0.4333°, 31.2333°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 7295.16 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 2515674.62 km²", |
| "FINAL ANSWER: Area: 2515674.62 km², Perimeter: 7295.16 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 15.26349, |
| "lon": 74.10875, |
| "name": "Curchorem" |
| }, |
| { |
| "lat": 27.52698, |
| "lon": 80.75461, |
| "name": "Khairābād" |
| }, |
| { |
| "lat": 22.642, |
| "lon": 90.42598, |
| "name": "Charāmaddi" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 856990.63, |
| "perimeter_km": 4541.17, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Curchorem: (15.2635°, 74.1088°)", |
| " Khairābād: (27.5270°, 80.7546°)", |
| " Charāmaddi: (22.6420°, 90.4260°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4541.17 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 856990.63 km²", |
| "FINAL ANSWER: Area: 856990.63 km², Perimeter: 4541.17 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": -30.50123, |
| "lon": 151.66553, |
| "name": "Armidale" |
| }, |
| { |
| "lat": -27.20338, |
| "lon": 152.95923, |
| "name": "Narangba" |
| }, |
| { |
| "lat": -27.98941, |
| "lon": 153.33633, |
| "name": "Nerang" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 12226.39, |
| "perimeter_km": 805.63, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Armidale: (-30.5012°, 151.6655°)", |
| " Narangba: (-27.2034°, 152.9592°)", |
| " Nerang: (-27.9894°, 153.3363°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 805.63 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 12226.39 km²", |
| "FINAL ANSWER: Area: 12226.39 km², Perimeter: 805.63 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": -22.27407, |
| "lon": 166.44884, |
| "name": "Nouméa" |
| }, |
| { |
| "lat": -36.88745, |
| "lon": 174.77059, |
| "name": "Epsom" |
| }, |
| { |
| "lat": -44.39672, |
| "lon": 171.25364, |
| "name": "Timaru" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 595347.33, |
| "perimeter_km": 5196.15, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Nouméa: (-22.2741°, 166.4488°)", |
| " Epsom: (-36.8875°, 174.7706°)", |
| " Timaru: (-44.3967°, 171.2536°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5196.15 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 595347.33 km²", |
| "FINAL ANSWER: Area: 595347.33 km², Perimeter: 5196.15 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 37.18516, |
| "lon": -5.78093, |
| "name": "Utrera" |
| }, |
| { |
| "lat": 43.66228, |
| "lon": -7.59344, |
| "name": "Viveiro" |
| }, |
| { |
| "lat": 53.56507, |
| "lon": -2.12267, |
| "name": "Royton" |
| }, |
| { |
| "lat": 50.54322, |
| "lon": 7.1113, |
| "name": "Bad Neuenahr-Ahrweiler" |
| }, |
| { |
| "lat": 42.21389, |
| "lon": 20.73972, |
| "name": "Prizren" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 2133220.45, |
| "perimeter_km": 6341.52, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Utrera: (37.1852°, -5.7809°)", |
| " Viveiro: (43.6623°, -7.5934°)", |
| " Royton: (53.5651°, -2.1227°)", |
| " Bad Neuenahr-Ahrweiler: (50.5432°, 7.1113°)", |
| " Prizren: (42.2139°, 20.7397°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 6341.52 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 2133220.45 km²", |
| "FINAL ANSWER: Area: 2133220.45 km², Perimeter: 6341.52 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 9.28358, |
| "lon": 76.45519, |
| "name": "Haripād" |
| }, |
| { |
| "lat": 16.9985, |
| "lon": 79.9656, |
| "name": "Kodār" |
| }, |
| { |
| "lat": 22.06312, |
| "lon": 82.13129, |
| "name": "Tifrā" |
| }, |
| { |
| "lat": 26.97982, |
| "lon": 84.85065, |
| "name": "Raxaul" |
| }, |
| { |
| "lat": 25.10479, |
| "lon": 84.1162, |
| "name": "Nokha" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 57521.94, |
| "perimeter_km": 4315.21, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Haripād: (9.2836°, 76.4552°)", |
| " Kodār: (16.9985°, 79.9656°)", |
| " Tifrā: (22.0631°, 82.1313°)", |
| " Raxaul: (26.9798°, 84.8507°)", |
| " Nokha: (25.1048°, 84.1162°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4315.21 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 57521.94 km²", |
| "FINAL ANSWER: Area: 57521.94 km², Perimeter: 4315.21 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": -35.28346, |
| "lon": 149.12807, |
| "name": "Canberra" |
| }, |
| { |
| "lat": -37.6, |
| "lon": 144.95, |
| "name": "Craigieburn" |
| }, |
| { |
| "lat": -30.50123, |
| "lon": 151.66553, |
| "name": "Armidale" |
| }, |
| { |
| "lat": -27.94402, |
| "lon": 153.39815, |
| "name": "Labrador" |
| }, |
| { |
| "lat": -30.29626, |
| "lon": 153.11351, |
| "name": "Coffs Harbour" |
| }, |
| { |
| "lat": -33.82346, |
| "lon": 150.94607, |
| "name": "Greystanes" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 132792.89, |
| "perimeter_km": 2724.15, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Canberra: (-35.2835°, 149.1281°)", |
| " Craigieburn: (-37.6000°, 144.9500°)", |
| " Armidale: (-30.5012°, 151.6655°)", |
| " Labrador: (-27.9440°, 153.3981°)", |
| " Coffs Harbour: (-30.2963°, 153.1135°)", |
| " Greystanes: (-33.8235°, 150.9461°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2724.15 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 132792.89 km²", |
| "FINAL ANSWER: Area: 132792.89 km², Perimeter: 2724.15 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": -19.86528, |
| "lon": -47.44, |
| "name": "Sacramento" |
| }, |
| { |
| "lat": -0.826, |
| "lon": -52.506, |
| "name": "Laranjal do Jari" |
| }, |
| { |
| "lat": -7.03306, |
| "lon": -35.85722, |
| "name": "Esperança" |
| }, |
| { |
| "lat": -16.575, |
| "lon": -39.55333, |
| "name": "Itabela" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 2126556.12, |
| "perimeter_km": 6202.58, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Sacramento: (-19.8653°, -47.4400°)", |
| " Laranjal do Jari: (-0.8260°, -52.5060°)", |
| " Esperança: (-7.0331°, -35.8572°)", |
| " Itabela: (-16.5750°, -39.5533°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 6202.58 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 2126556.12 km²", |
| "FINAL ANSWER: Area: 2126556.12 km², Perimeter: 6202.58 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": -37.9, |
| "lon": 145.18333, |
| "name": "Wheelers Hill" |
| }, |
| { |
| "lat": -33.41665, |
| "lon": 149.5806, |
| "name": "Bathurst" |
| }, |
| { |
| "lat": -28.07071, |
| "lon": 153.39329, |
| "name": "Robina" |
| }, |
| { |
| "lat": -33.8188, |
| "lon": 151.1062, |
| "name": "Ryde" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 131897.47, |
| "perimeter_km": 2709.96, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Wheelers Hill: (-37.9000°, 145.1833°)", |
| " Bathurst: (-33.4166°, 149.5806°)", |
| " Robina: (-28.0707°, 153.3933°)", |
| " Ryde: (-33.8188°, 151.1062°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2709.96 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 131897.47 km²", |
| "FINAL ANSWER: Area: 131897.47 km², Perimeter: 2709.96 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": 32.46181, |
| "lon": -90.11536, |
| "name": "Madison" |
| }, |
| { |
| "lat": 32.54208, |
| "lon": -97.32085, |
| "name": "Burleson" |
| }, |
| { |
| "lat": 39.83665, |
| "lon": -105.0372, |
| "name": "Westminster" |
| }, |
| { |
| "lat": 42.50309, |
| "lon": -83.18354, |
| "name": "Berkley" |
| }, |
| { |
| "lat": 42.19454, |
| "lon": -71.83563, |
| "name": "Auburn" |
| }, |
| { |
| "lat": 30.36576, |
| "lon": -88.55613, |
| "name": "Pascagoula" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 2051963.85, |
| "perimeter_km": 6785.01, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Madison: (32.4618°, -90.1154°)", |
| " Burleson: (32.5421°, -97.3208°)", |
| " Westminster: (39.8366°, -105.0372°)", |
| " Berkley: (42.5031°, -83.1835°)", |
| " Auburn: (42.1945°, -71.8356°)", |
| " Pascagoula: (30.3658°, -88.5561°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 6785.01 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 2051963.85 km²", |
| "FINAL ANSWER: Area: 2051963.85 km², Perimeter: 6785.01 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 47.30707, |
| "lon": 11.06817, |
| "name": "Telfs" |
| }, |
| { |
| "lat": 52.21667, |
| "lon": -0.26667, |
| "name": "Saint Neots" |
| }, |
| { |
| "lat": 53.0, |
| "lon": -1.13333, |
| "name": "Arnold" |
| }, |
| { |
| "lat": 56.04284, |
| "lon": 37.85153, |
| "name": "Zavety Il’icha" |
| }, |
| { |
| "lat": 53.22186, |
| "lon": 26.67679, |
| "name": "Nesvizh" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1158059.26, |
| "perimeter_km": 5657.05, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Telfs: (47.3071°, 11.0682°)", |
| " Saint Neots: (52.2167°, -0.2667°)", |
| " Arnold: (53.0000°, -1.1333°)", |
| " Zavety Il’icha: (56.0428°, 37.8515°)", |
| " Nesvizh: (53.2219°, 26.6768°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5657.05 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1158059.26 km²", |
| "FINAL ANSWER: Area: 1158059.26 km², Perimeter: 5657.05 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": -37.81992, |
| "lon": 145.0358, |
| "name": "Hawthorn" |
| }, |
| { |
| "lat": -38.38176, |
| "lon": 142.48799, |
| "name": "Warrnambool" |
| }, |
| { |
| "lat": -27.62329, |
| "lon": 153.04785, |
| "name": "Calamvale" |
| }, |
| { |
| "lat": -32.73308, |
| "lon": 151.5574, |
| "name": "Maitland" |
| }, |
| { |
| "lat": -33.9049, |
| "lon": 151.01996, |
| "name": "Yagoona" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 240031.73, |
| "perimeter_km": 3196.88, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Hawthorn: (-37.8199°, 145.0358°)", |
| " Warrnambool: (-38.3818°, 142.4880°)", |
| " Calamvale: (-27.6233°, 153.0479°)", |
| " Maitland: (-32.7331°, 151.5574°)", |
| " Yagoona: (-33.9049°, 151.0200°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3196.88 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 240031.73 km²", |
| "FINAL ANSWER: Area: 240031.73 km², Perimeter: 3196.88 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 43.27766, |
| "lon": 5.43133, |
| "name": "Saint-Loup" |
| }, |
| { |
| "lat": 50.88637, |
| "lon": 7.0583, |
| "name": "Porz am Rhein" |
| }, |
| { |
| "lat": 52.48419, |
| "lon": 13.53185, |
| "name": "Karlshorst" |
| }, |
| { |
| "lat": 48.20906, |
| "lon": 16.37135, |
| "name": "Innere Stadt" |
| }, |
| { |
| "lat": 40.53123, |
| "lon": 17.58522, |
| "name": "Francavilla Fontana" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 834492.12, |
| "perimeter_km": 3760.44, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Saint-Loup: (43.2777°, 5.4313°)", |
| " Porz am Rhein: (50.8864°, 7.0583°)", |
| " Karlshorst: (52.4842°, 13.5319°)", |
| " Innere Stadt: (48.2091°, 16.3713°)", |
| " Francavilla Fontana: (40.5312°, 17.5852°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3760.44 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 834492.12 km²", |
| "FINAL ANSWER: Area: 834492.12 km², Perimeter: 3760.44 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": 5.06191, |
| "lon": -6.25997, |
| "name": "Sahoua" |
| }, |
| { |
| "lat": 6.13656, |
| "lon": -6.84096, |
| "name": "Loboville" |
| }, |
| { |
| "lat": 8.56744, |
| "lon": -10.1336, |
| "name": "Gueckedou" |
| }, |
| { |
| "lat": 14.78148, |
| "lon": -17.3841, |
| "name": "N’diareme limamoulaye" |
| }, |
| { |
| "lat": 6.9827, |
| "lon": 7.45534, |
| "name": "Enugu-Ezike" |
| }, |
| { |
| "lat": 5.35444, |
| "lon": -4.00167, |
| "name": "Abidjan" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1007828.31, |
| "perimeter_km": 6013.42, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Sahoua: (5.0619°, -6.2600°)", |
| " Loboville: (6.1366°, -6.8410°)", |
| " Gueckedou: (8.5674°, -10.1336°)", |
| " N’diareme limamoulaye: (14.7815°, -17.3841°)", |
| " Enugu-Ezike: (6.9827°, 7.4553°)", |
| " Abidjan: (5.3544°, -4.0017°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 6013.42 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1007828.31 km²", |
| "FINAL ANSWER: Area: 1007828.31 km², Perimeter: 6013.42 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 52.10894, |
| "lon": 23.71749, |
| "name": "Brest" |
| }, |
| { |
| "lat": 52.42719, |
| "lon": 22.86231, |
| "name": "Siemiatycze" |
| }, |
| { |
| "lat": 55.84376, |
| "lon": 48.51784, |
| "name": "Zelenodolsk" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 47203.07, |
| "perimeter_km": 3435.73, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Brest: (52.1089°, 23.7175°)", |
| " Siemiatycze: (52.4272°, 22.8623°)", |
| " Zelenodolsk: (55.8438°, 48.5178°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3435.73 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 47203.07 km²", |
| "FINAL ANSWER: Area: 47203.07 km², Perimeter: 3435.73 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": -38.08333, |
| "lon": 144.38333, |
| "name": "Corio" |
| }, |
| { |
| "lat": -34.92866, |
| "lon": 138.59863, |
| "name": "Adelaide" |
| }, |
| { |
| "lat": -34.06564, |
| "lon": 151.01266, |
| "name": "Engadine" |
| }, |
| { |
| "lat": -37.81667, |
| "lon": 145.23333, |
| "name": "Ringwood" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 222012.71, |
| "perimeter_km": 2512.33, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Corio: (-38.0833°, 144.3833°)", |
| " Adelaide: (-34.9287°, 138.5986°)", |
| " Engadine: (-34.0656°, 151.0127°)", |
| " Ringwood: (-37.8167°, 145.2333°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2512.33 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 222012.71 km²", |
| "FINAL ANSWER: Area: 222012.71 km², Perimeter: 2512.33 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 37.5992, |
| "lon": -1.31493, |
| "name": "Mazarrón" |
| }, |
| { |
| "lat": 51.62127, |
| "lon": 0.30556, |
| "name": "Brentwood" |
| }, |
| { |
| "lat": 48.85442, |
| "lon": 2.48268, |
| "name": "Fontenay-sous-Bois" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 146464.62, |
| "perimeter_km": 3197.09, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Mazarrón: (37.5992°, -1.3149°)", |
| " Brentwood: (51.6213°, 0.3056°)", |
| " Fontenay-sous-Bois: (48.8544°, 2.4827°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3197.09 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 146464.62 km²", |
| "FINAL ANSWER: Area: 146464.62 km², Perimeter: 3197.09 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 52.30273, |
| "lon": -0.69446, |
| "name": "Wellingborough" |
| }, |
| { |
| "lat": 55.79916, |
| "lon": -4.39285, |
| "name": "Barrhead" |
| }, |
| { |
| "lat": 48.9685, |
| "lon": 8.30704, |
| "name": "Rheinstetten" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 91548.72, |
| "perimeter_km": 2337.59, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Wellingborough: (52.3027°, -0.6945°)", |
| " Barrhead: (55.7992°, -4.3929°)", |
| " Rheinstetten: (48.9685°, 8.3070°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2337.59 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 91548.72 km²", |
| "FINAL ANSWER: Area: 91548.72 km², Perimeter: 2337.59 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": 27.59178, |
| "lon": 68.61848, |
| "name": "Pir Jo Goth" |
| }, |
| { |
| "lat": 28.86993, |
| "lon": 75.9165, |
| "name": "Toshām" |
| }, |
| { |
| "lat": 40.7046, |
| "lon": 72.86666, |
| "name": "Kara Suu" |
| }, |
| { |
| "lat": 27.47315, |
| "lon": 78.3031, |
| "name": "Jalesar" |
| }, |
| { |
| "lat": 19.77889, |
| "lon": 85.17033, |
| "name": "Bānapur" |
| }, |
| { |
| "lat": 18.42866, |
| "lon": 79.86385, |
| "name": "Bhupalpally" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1959617.68, |
| "perimeter_km": 6844.43, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Pir Jo Goth: (27.5918°, 68.6185°)", |
| " Toshām: (28.8699°, 75.9165°)", |
| " Kara Suu: (40.7046°, 72.8667°)", |
| " Jalesar: (27.4732°, 78.3031°)", |
| " Bānapur: (19.7789°, 85.1703°)", |
| " Bhupalpally: (18.4287°, 79.8638°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 6844.43 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1959617.68 km²", |
| "FINAL ANSWER: Area: 1959617.68 km², Perimeter: 6844.43 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": 40.42118, |
| "lon": -79.7881, |
| "name": "Monroeville" |
| }, |
| { |
| "lat": 37.77422, |
| "lon": -87.11333, |
| "name": "Owensboro" |
| }, |
| { |
| "lat": 42.24481, |
| "lon": -83.06095, |
| "name": "LaSalle" |
| }, |
| { |
| "lat": 43.65498, |
| "lon": -79.37153, |
| "name": "Moss Park" |
| }, |
| { |
| "lat": 42.81259, |
| "lon": -70.87728, |
| "name": "Newburyport" |
| }, |
| { |
| "lat": 41.39482, |
| "lon": -73.45401, |
| "name": "Danbury" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 314274.72, |
| "perimeter_km": 3142.56, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Monroeville: (40.4212°, -79.7881°)", |
| " Owensboro: (37.7742°, -87.1133°)", |
| " LaSalle: (42.2448°, -83.0610°)", |
| " Moss Park: (43.6550°, -79.3715°)", |
| " Newburyport: (42.8126°, -70.8773°)", |
| " Danbury: (41.3948°, -73.4540°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3142.56 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 314274.72 km²", |
| "FINAL ANSWER: Area: 314274.72 km², Perimeter: 3142.56 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 32.82346, |
| "lon": -97.17057, |
| "name": "Hurst" |
| }, |
| { |
| "lat": 39.95087, |
| "lon": -86.26194, |
| "name": "Zionsville" |
| }, |
| { |
| "lat": 45.46536, |
| "lon": -73.66585, |
| "name": "Côte-Saint-Luc" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 10007.16, |
| "perimeter_km": 4903.79, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Hurst: (32.8235°, -97.1706°)", |
| " Zionsville: (39.9509°, -86.2619°)", |
| " Côte-Saint-Luc: (45.4654°, -73.6659°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4903.79 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 10007.16 km²", |
| "FINAL ANSWER: Area: 10007.16 km², Perimeter: 4903.79 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 7.73909, |
| "lon": -7.61377, |
| "name": "Biankouma" |
| }, |
| { |
| "lat": 9.50511, |
| "lon": -7.56433, |
| "name": "Odienné" |
| }, |
| { |
| "lat": 12.70354, |
| "lon": -7.96463, |
| "name": "Dialakorodji" |
| }, |
| { |
| "lat": 5.51737, |
| "lon": 5.75006, |
| "name": "Warri" |
| }, |
| { |
| "lat": 6.38423, |
| "lon": -3.88759, |
| "name": "Akoupé" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 475546.23, |
| "perimeter_km": 3766.52, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Biankouma: (7.7391°, -7.6138°)", |
| " Odienné: (9.5051°, -7.5643°)", |
| " Dialakorodji: (12.7035°, -7.9646°)", |
| " Warri: (5.5174°, 5.7501°)", |
| " Akoupé: (6.3842°, -3.8876°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3766.52 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 475546.23 km²", |
| "FINAL ANSWER: Area: 475546.23 km², Perimeter: 3766.52 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 40.25038, |
| "lon": -3.83062, |
| "name": "Humanes de Madrid" |
| }, |
| { |
| "lat": 53.10434, |
| "lon": -2.02207, |
| "name": "Leek" |
| }, |
| { |
| "lat": 52.25, |
| "lon": -0.88333, |
| "name": "Northampton" |
| }, |
| { |
| "lat": 51.87819, |
| "lon": 0.55292, |
| "name": "Braintree" |
| }, |
| { |
| "lat": 49.05, |
| "lon": 2.1, |
| "name": "Pontoise" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 264903.53, |
| "perimeter_km": 3081.77, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Humanes de Madrid: (40.2504°, -3.8306°)", |
| " Leek: (53.1043°, -2.0221°)", |
| " Northampton: (52.2500°, -0.8833°)", |
| " Braintree: (51.8782°, 0.5529°)", |
| " Pontoise: (49.0500°, 2.1000°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3081.77 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 264903.53 km²", |
| "FINAL ANSWER: Area: 264903.53 km², Perimeter: 3081.77 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 32.89953, |
| "lon": -105.96027, |
| "name": "Alamogordo" |
| }, |
| { |
| "lat": 43.88441, |
| "lon": -91.23514, |
| "name": "Onalaska" |
| }, |
| { |
| "lat": 41.95781, |
| "lon": -87.76506, |
| "name": "Portage Park" |
| }, |
| { |
| "lat": 37.13179, |
| "lon": -80.57645, |
| "name": "Radford" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1012859.06, |
| "perimeter_km": 5289.45, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Alamogordo: (32.8995°, -105.9603°)", |
| " Onalaska: (43.8844°, -91.2351°)", |
| " Portage Park: (41.9578°, -87.7651°)", |
| " Radford: (37.1318°, -80.5764°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5289.45 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1012859.06 km²", |
| "FINAL ANSWER: Area: 1012859.06 km², Perimeter: 5289.45 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 36.67774, |
| "lon": -121.6555, |
| "name": "Salinas" |
| }, |
| { |
| "lat": 49.16667, |
| "lon": -123.13333, |
| "name": "Brighouse-City Centre" |
| }, |
| { |
| "lat": 49.88307, |
| "lon": -119.48568, |
| "name": "Kelowna" |
| }, |
| { |
| "lat": 34.05168, |
| "lon": -117.9684, |
| "name": "West Puente Valley" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 461940.66, |
| "perimeter_km": 3877.44, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Salinas: (36.6777°, -121.6555°)", |
| " Brighouse-City Centre: (49.1667°, -123.1333°)", |
| " Kelowna: (49.8831°, -119.4857°)", |
| " West Puente Valley: (34.0517°, -117.9684°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3877.44 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 461940.66 km²", |
| "FINAL ANSWER: Area: 461940.66 km², Perimeter: 3877.44 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": -34.42603, |
| "lon": -58.57962, |
| "name": "Tigre" |
| }, |
| { |
| "lat": -23.31028, |
| "lon": -51.16278, |
| "name": "Londrina" |
| }, |
| { |
| "lat": -22.75361, |
| "lon": -47.41361, |
| "name": "Santa Bárbara d'Oeste" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 223433.28, |
| "perimeter_km": 3511.49, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Tigre: (-34.4260°, -58.5796°)", |
| " Londrina: (-23.3103°, -51.1628°)", |
| " Santa Bárbara d'Oeste: (-22.7536°, -47.4136°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3511.49 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 223433.28 km²", |
| "FINAL ANSWER: Area: 223433.28 km², Perimeter: 3511.49 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 50.46198, |
| "lon": -3.52522, |
| "name": "Torquay" |
| }, |
| { |
| "lat": 50.66667, |
| "lon": 3.08333, |
| "name": "Marcq-en-Barœul" |
| }, |
| { |
| "lat": 52.25917, |
| "lon": 4.75972, |
| "name": "Aalsmeer" |
| }, |
| { |
| "lat": 43.8805, |
| "lon": 11.09699, |
| "name": "Prato" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 351585.22, |
| "perimeter_km": 3043.87, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Torquay: (50.4620°, -3.5252°)", |
| " Marcq-en-Barœul: (50.6667°, 3.0833°)", |
| " Aalsmeer: (52.2592°, 4.7597°)", |
| " Prato: (43.8805°, 11.0970°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3043.87 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 351585.22 km²", |
| "FINAL ANSWER: Area: 351585.22 km², Perimeter: 3043.87 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": -25.44613, |
| "lon": -56.43928, |
| "name": "Coronel Oviedo" |
| }, |
| { |
| "lat": -20.78765, |
| "lon": -51.70338, |
| "name": "Três Lagoas" |
| }, |
| { |
| "lat": -12.67, |
| "lon": -39.10194, |
| "name": "Cruz das Almas" |
| }, |
| { |
| "lat": -22.11667, |
| "lon": -43.20917, |
| "name": "Três Rios" |
| }, |
| { |
| "lat": -23.53936, |
| "lon": -46.51788, |
| "name": "Vila Matilde" |
| }, |
| { |
| "lat": -22.97056, |
| "lon": -46.99583, |
| "name": "Valinhos" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 836083.18, |
| "perimeter_km": 4912.14, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Coronel Oviedo: (-25.4461°, -56.4393°)", |
| " Três Lagoas: (-20.7876°, -51.7034°)", |
| " Cruz das Almas: (-12.6700°, -39.1019°)", |
| " Três Rios: (-22.1167°, -43.2092°)", |
| " Vila Matilde: (-23.5394°, -46.5179°)", |
| " Valinhos: (-22.9706°, -46.9958°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4912.14 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 836083.18 km²", |
| "FINAL ANSWER: Area: 836083.18 km², Perimeter: 4912.14 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 38.25424, |
| "lon": -85.75941, |
| "name": "Louisville" |
| }, |
| { |
| "lat": 40.4284, |
| "lon": -79.69755, |
| "name": "Murrysville" |
| }, |
| { |
| "lat": 40.57927, |
| "lon": -74.41154, |
| "name": "South Plainfield" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 42072.45, |
| "perimeter_km": 2029.33, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Louisville: (38.2542°, -85.7594°)", |
| " Murrysville: (40.4284°, -79.6976°)", |
| " South Plainfield: (40.5793°, -74.4115°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2029.33 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 42072.45 km²", |
| "FINAL ANSWER: Area: 42072.45 km², Perimeter: 2029.33 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 38.70712, |
| "lon": -121.28106, |
| "name": "Citrus Heights" |
| }, |
| { |
| "lat": 49.02049, |
| "lon": -122.79507, |
| "name": "White Rock" |
| }, |
| { |
| "lat": 51.03951, |
| "lon": -114.07087, |
| "name": "Beltline" |
| }, |
| { |
| "lat": 33.77974, |
| "lon": -116.46529, |
| "name": "Cathedral City" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 817970.23, |
| "perimeter_km": 4441.4, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Citrus Heights: (38.7071°, -121.2811°)", |
| " White Rock: (49.0205°, -122.7951°)", |
| " Beltline: (51.0395°, -114.0709°)", |
| " Cathedral City: (33.7797°, -116.4653°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4441.40 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 817970.23 km²", |
| "FINAL ANSWER: Area: 817970.23 km², Perimeter: 4441.40 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 48.40821, |
| "lon": 33.70919, |
| "name": "Pyatykhatky" |
| }, |
| { |
| "lat": 49.02894, |
| "lon": 33.43847, |
| "name": "Kriukiv" |
| }, |
| { |
| "lat": 59.15838, |
| "lon": 57.5705, |
| "name": "Aleksandrovsk" |
| }, |
| { |
| "lat": 56.44222, |
| "lon": 60.18778, |
| "name": "Polevskoy" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 395007.51, |
| "perimeter_km": 4317.38, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Pyatykhatky: (48.4082°, 33.7092°)", |
| " Kriukiv: (49.0289°, 33.4385°)", |
| " Aleksandrovsk: (59.1584°, 57.5705°)", |
| " Polevskoy: (56.4422°, 60.1878°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4317.38 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 395007.51 km²", |
| "FINAL ANSWER: Area: 395007.51 km², Perimeter: 4317.38 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 51.75, |
| "lon": -2.2, |
| "name": "Stroud" |
| }, |
| { |
| "lat": 53.29483, |
| "lon": -3.72674, |
| "name": "Colwyn Bay" |
| }, |
| { |
| "lat": 55.94433, |
| "lon": -4.57061, |
| "name": "Dumbarton" |
| }, |
| { |
| "lat": 41.91886, |
| "lon": 8.73812, |
| "name": "Ajaccio" |
| }, |
| { |
| "lat": 43.31083, |
| "lon": 3.47583, |
| "name": "Agde" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 329084.4, |
| "perimeter_km": 3818.07, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Stroud: (51.7500°, -2.2000°)", |
| " Colwyn Bay: (53.2948°, -3.7267°)", |
| " Dumbarton: (55.9443°, -4.5706°)", |
| " Ajaccio: (41.9189°, 8.7381°)", |
| " Agde: (43.3108°, 3.4758°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3818.07 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 329084.40 km²", |
| "FINAL ANSWER: Area: 329084.40 km², Perimeter: 3818.07 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 33.79833, |
| "lon": 117.86639, |
| "name": "Guanshan" |
| }, |
| { |
| "lat": 35.63333, |
| "lon": 134.63333, |
| "name": "Kasumi" |
| }, |
| { |
| "lat": 35.48333, |
| "lon": 136.91667, |
| "name": "Sekimachi" |
| }, |
| { |
| "lat": 34.92633, |
| "lon": 134.84533, |
| "name": "Kasai" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 69619.31, |
| "perimeter_km": 3511.1, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Guanshan: (33.7983°, 117.8664°)", |
| " Kasumi: (35.6333°, 134.6333°)", |
| " Sekimachi: (35.4833°, 136.9167°)", |
| " Kasai: (34.9263°, 134.8453°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3511.10 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 69619.31 km²", |
| "FINAL ANSWER: Area: 69619.31 km², Perimeter: 3511.10 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 19.09457, |
| "lon": 74.73843, |
| "name": "Ahilyanagar" |
| }, |
| { |
| "lat": 21.62878, |
| "lon": 69.63386, |
| "name": "Chhaya" |
| }, |
| { |
| "lat": 24.89843, |
| "lon": 88.52844, |
| "name": "Mohāmmadpur" |
| }, |
| { |
| "lat": 22.88333, |
| "lon": 87.78333, |
| "name": "Arāmbāgh" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 532099.4, |
| "perimeter_km": 4218.55, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Ahilyanagar: (19.0946°, 74.7384°)", |
| " Chhaya: (21.6288°, 69.6339°)", |
| " Mohāmmadpur: (24.8984°, 88.5284°)", |
| " Arāmbāgh: (22.8833°, 87.7833°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4218.55 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 532099.40 km²", |
| "FINAL ANSWER: Area: 532099.40 km², Perimeter: 4218.55 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 10.86225, |
| "lon": 0.20762, |
| "name": "Dapaong" |
| }, |
| { |
| "lat": 14.00776, |
| "lon": 0.75306, |
| "name": "Téra" |
| }, |
| { |
| "lat": 5.20131, |
| "lon": 7.98373, |
| "name": "Itu" |
| }, |
| { |
| "lat": 7.49748, |
| "lon": 5.23041, |
| "name": "Ikere-Ekiti" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 181981.69, |
| "perimeter_km": 2677.53, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Dapaong: (10.8622°, 0.2076°)", |
| " Téra: (14.0078°, 0.7531°)", |
| " Itu: (5.2013°, 7.9837°)", |
| " Ikere-Ekiti: (7.4975°, 5.2304°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2677.53 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 181981.69 km²", |
| "FINAL ANSWER: Area: 181981.69 km², Perimeter: 2677.53 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": -37.62581, |
| "lon": 144.92555, |
| "name": "Roxburgh Park" |
| }, |
| { |
| "lat": -27.22426, |
| "lon": 153.02075, |
| "name": "North Lakes" |
| }, |
| { |
| "lat": -28.07071, |
| "lon": 153.39329, |
| "name": "Robina" |
| }, |
| { |
| "lat": -33.73333, |
| "lon": 150.93284, |
| "name": "Glenwood" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 167629.23, |
| "perimeter_km": 2849.22, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Roxburgh Park: (-37.6258°, 144.9255°)", |
| " North Lakes: (-27.2243°, 153.0207°)", |
| " Robina: (-28.0707°, 153.3933°)", |
| " Glenwood: (-33.7333°, 150.9328°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2849.22 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 167629.23 km²", |
| "FINAL ANSWER: Area: 167629.23 km², Perimeter: 2849.22 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 55.7068, |
| "lon": 21.13912, |
| "name": "Klaipėda" |
| }, |
| { |
| "lat": 66.31278, |
| "lon": 14.14278, |
| "name": "Mo i Rana" |
| }, |
| { |
| "lat": 56.01931, |
| "lon": 39.94848, |
| "name": "Lakinsk" |
| }, |
| { |
| "lat": 55.59525, |
| "lon": 37.05235, |
| "name": "Krasnoznamensk" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 762137.04, |
| "perimeter_km": 4192.89, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Klaipėda: (55.7068°, 21.1391°)", |
| " Mo i Rana: (66.3128°, 14.1428°)", |
| " Lakinsk: (56.0193°, 39.9485°)", |
| " Krasnoznamensk: (55.5953°, 37.0523°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4192.89 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 762137.04 km²", |
| "FINAL ANSWER: Area: 762137.04 km², Perimeter: 4192.89 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 48.84133, |
| "lon": -123.68596, |
| "name": "North Cowichan" |
| }, |
| { |
| "lat": 47.97898, |
| "lon": -122.20208, |
| "name": "Everett" |
| }, |
| { |
| "lat": 49.15531, |
| "lon": -123.15706, |
| "name": "Blundell" |
| }, |
| { |
| "lat": 47.50024, |
| "lon": -111.30081, |
| "name": "Great Falls" |
| }, |
| { |
| "lat": 34.25223, |
| "lon": -118.28841, |
| "name": "Tujunga" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 749630.99, |
| "perimeter_km": 4455.16, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " North Cowichan: (48.8413°, -123.6860°)", |
| " Everett: (47.9790°, -122.2021°)", |
| " Blundell: (49.1553°, -123.1571°)", |
| " Great Falls: (47.5002°, -111.3008°)", |
| " Tujunga: (34.2522°, -118.2884°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4455.16 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 749630.99 km²", |
| "FINAL ANSWER: Area: 749630.99 km², Perimeter: 4455.16 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 49.2818, |
| "lon": 9.68352, |
| "name": "Künzelsau" |
| }, |
| { |
| "lat": 48.21563, |
| "lon": 18.60705, |
| "name": "Levice" |
| }, |
| { |
| "lat": 35.0125, |
| "lon": 34.05833, |
| "name": "Protaras" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 325842.86, |
| "perimeter_km": 5148.56, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Künzelsau: (49.2818°, 9.6835°)", |
| " Levice: (48.2156°, 18.6071°)", |
| " Protaras: (35.0125°, 34.0583°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5148.56 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 325842.86 km²", |
| "FINAL ANSWER: Area: 325842.86 km², Perimeter: 5148.56 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 37.3925, |
| "lon": 126.92694, |
| "name": "Anyang-si" |
| }, |
| { |
| "lat": 40.9241, |
| "lon": 122.80437, |
| "name": "Nantai" |
| }, |
| { |
| "lat": 44.02127, |
| "lon": 144.26971, |
| "name": "Abashiri" |
| }, |
| { |
| "lat": 34.68505, |
| "lon": 135.80485, |
| "name": "Nara-shi" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 966465.76, |
| "perimeter_km": 4437.06, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Anyang-si: (37.3925°, 126.9269°)", |
| " Nantai: (40.9241°, 122.8044°)", |
| " Abashiri: (44.0213°, 144.2697°)", |
| " Nara-shi: (34.6850°, 135.8048°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4437.06 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 966465.76 km²", |
| "FINAL ANSWER: Area: 966465.76 km², Perimeter: 4437.06 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": -36.8582, |
| "lon": 174.62019, |
| "name": "Lincoln" |
| }, |
| { |
| "lat": -37.78333, |
| "lon": 175.28333, |
| "name": "Hamilton" |
| }, |
| { |
| "lat": -40.91667, |
| "lon": 175.01667, |
| "name": "Paraparaumu" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 11435.67, |
| "perimeter_km": 920.16, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Lincoln: (-36.8582°, 174.6202°)", |
| " Hamilton: (-37.7833°, 175.2833°)", |
| " Paraparaumu: (-40.9167°, 175.0167°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 920.16 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 11435.67 km²", |
| "FINAL ANSWER: Area: 11435.67 km², Perimeter: 920.16 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": 41.54211, |
| "lon": 2.4445, |
| "name": "Mataró" |
| }, |
| { |
| "lat": 39.98567, |
| "lon": -0.04935, |
| "name": "Castelló de la Plana" |
| }, |
| { |
| "lat": 38.69875, |
| "lon": -9.19289, |
| "name": "Belém" |
| }, |
| { |
| "lat": 51.23228, |
| "lon": -0.3338, |
| "name": "Dorking" |
| }, |
| { |
| "lat": 45.44694, |
| "lon": 8.62118, |
| "name": "Novara" |
| }, |
| { |
| "lat": 46.71332, |
| "lon": 20.14241, |
| "name": "Csongrád" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1065204.39, |
| "perimeter_km": 5968.07, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Mataró: (41.5421°, 2.4445°)", |
| " Castelló de la Plana: (39.9857°, -0.0493°)", |
| " Belém: (38.6987°, -9.1929°)", |
| " Dorking: (51.2323°, -0.3338°)", |
| " Novara: (45.4469°, 8.6212°)", |
| " Csongrád: (46.7133°, 20.1424°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5968.07 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1065204.39 km²", |
| "FINAL ANSWER: Area: 1065204.39 km², Perimeter: 5968.07 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 38.70102, |
| "lon": -9.17145, |
| "name": "Alcântara" |
| }, |
| { |
| "lat": 46.34015, |
| "lon": 2.60254, |
| "name": "Montluçon" |
| }, |
| { |
| "lat": 47.42642, |
| "lon": 9.65851, |
| "name": "Lustenau" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 133041.89, |
| "perimeter_km": 3636.74, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Alcântara: (38.7010°, -9.1715°)", |
| " Montluçon: (46.3402°, 2.6025°)", |
| " Lustenau: (47.4264°, 9.6585°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3636.74 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 133041.89 km²", |
| "FINAL ANSWER: Area: 133041.89 km², Perimeter: 3636.74 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": -29.66917, |
| "lon": -52.78889, |
| "name": "Candelária" |
| }, |
| { |
| "lat": -28.2925, |
| "lon": -53.50167, |
| "name": "Panambi" |
| }, |
| { |
| "lat": -23.15306, |
| "lon": -47.05778, |
| "name": "Itupeva" |
| }, |
| { |
| "lat": -20.10667, |
| "lon": -43.04889, |
| "name": "Alvinópolis" |
| }, |
| { |
| "lat": -23.45947, |
| "lon": -46.64086, |
| "name": "Mandaqui" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 154559.57, |
| "perimeter_km": 3012.76, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Candelária: (-29.6692°, -52.7889°)", |
| " Panambi: (-28.2925°, -53.5017°)", |
| " Itupeva: (-23.1531°, -47.0578°)", |
| " Alvinópolis: (-20.1067°, -43.0489°)", |
| " Mandaqui: (-23.4595°, -46.6409°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3012.76 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 154559.57 km²", |
| "FINAL ANSWER: Area: 154559.57 km², Perimeter: 3012.76 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 33.56504, |
| "lon": -117.72712, |
| "name": "Aliso Viejo" |
| }, |
| { |
| "lat": 37.36605, |
| "lon": -121.82718, |
| "name": "Alum Rock" |
| }, |
| { |
| "lat": 46.13817, |
| "lon": -122.93817, |
| "name": "Longview" |
| }, |
| { |
| "lat": 25.18909, |
| "lon": -99.82865, |
| "name": "Montemorelos" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1304882.65, |
| "perimeter_km": 6611.4, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Aliso Viejo: (33.5650°, -117.7271°)", |
| " Alum Rock: (37.3661°, -121.8272°)", |
| " Longview: (46.1382°, -122.9382°)", |
| " Montemorelos: (25.1891°, -99.8286°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 6611.40 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1304882.65 km²", |
| "FINAL ANSWER: Area: 1304882.65 km², Perimeter: 6611.40 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 22.56667, |
| "lon": 59.52889, |
| "name": "Sur" |
| }, |
| { |
| "lat": 26.26841, |
| "lon": 73.00594, |
| "name": "Jodhpur" |
| }, |
| { |
| "lat": 29.69197, |
| "lon": 76.98448, |
| "name": "Karnāl" |
| }, |
| { |
| "lat": 16.07786, |
| "lon": 75.81321, |
| "name": "Kamatgi" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1522808.94, |
| "perimeter_km": 5341.4, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Sur: (22.5667°, 59.5289°)", |
| " Jodhpur: (26.2684°, 73.0059°)", |
| " Karnāl: (29.6920°, 76.9845°)", |
| " Kamatgi: (16.0779°, 75.8132°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5341.40 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1522808.94 km²", |
| "FINAL ANSWER: Area: 1522808.94 km², Perimeter: 5341.40 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 39.5, |
| "lon": -0.35, |
| "name": "Alboraya" |
| }, |
| { |
| "lat": 54.4858, |
| "lon": 9.05239, |
| "name": "Husum" |
| }, |
| { |
| "lat": 51.31667, |
| "lon": 9.5, |
| "name": "Kassel" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 169135.55, |
| "perimeter_km": 3681.79, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Alboraya: (39.5000°, -0.3500°)", |
| " Husum: (54.4858°, 9.0524°)", |
| " Kassel: (51.3167°, 9.5000°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3681.79 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 169135.55 km²", |
| "FINAL ANSWER: Area: 169135.55 km², Perimeter: 3681.79 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": -27.46784, |
| "lon": -58.8344, |
| "name": "Corrientes" |
| }, |
| { |
| "lat": -26.8708, |
| "lon": -60.21537, |
| "name": "Quitilipi" |
| }, |
| { |
| "lat": -9.84139, |
| "lon": -39.48167, |
| "name": "Uauá" |
| }, |
| { |
| "lat": -22.87278, |
| "lon": -42.34306, |
| "name": "Araruama" |
| }, |
| { |
| "lat": -24.6925, |
| "lon": -48.00222, |
| "name": "Jacupiranga" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1299322.56, |
| "perimeter_km": 6252.03, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Corrientes: (-27.4678°, -58.8344°)", |
| " Quitilipi: (-26.8708°, -60.2154°)", |
| " Uauá: (-9.8414°, -39.4817°)", |
| " Araruama: (-22.8728°, -42.3431°)", |
| " Jacupiranga: (-24.6925°, -48.0022°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 6252.03 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1299322.56 km²", |
| "FINAL ANSWER: Area: 1299322.56 km², Perimeter: 6252.03 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 8.18122, |
| "lon": 9.74431, |
| "name": "Ibi" |
| }, |
| { |
| "lat": 12.15, |
| "lon": 27.35, |
| "name": "Ghubaysh" |
| }, |
| { |
| "lat": -2.55, |
| "lon": 33.03333, |
| "name": "Kisesa" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1734146.39, |
| "perimeter_km": 6572.18, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Ibi: (8.1812°, 9.7443°)", |
| " Ghubaysh: (12.1500°, 27.3500°)", |
| " Kisesa: (-2.5500°, 33.0333°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 6572.18 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1734146.39 km²", |
| "FINAL ANSWER: Area: 1734146.39 km², Perimeter: 6572.18 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": 37.07381, |
| "lon": 14.24038, |
| "name": "Gela" |
| }, |
| { |
| "lat": 41.97489, |
| "lon": 2.79281, |
| "name": "Salt" |
| }, |
| { |
| "lat": 43.16296, |
| "lon": 13.72274, |
| "name": "Fermo" |
| }, |
| { |
| "lat": 42.35861, |
| "lon": 20.825, |
| "name": "Suva Reka" |
| }, |
| { |
| "lat": 44.60789, |
| "lon": 40.10242, |
| "name": "Maykop" |
| }, |
| { |
| "lat": 37.96427, |
| "lon": 23.49649, |
| "name": "Salamína" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1130551.85, |
| "perimeter_km": 6573.37, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Gela: (37.0738°, 14.2404°)", |
| " Salt: (41.9749°, 2.7928°)", |
| " Fermo: (43.1630°, 13.7227°)", |
| " Suva Reka: (42.3586°, 20.8250°)", |
| " Maykop: (44.6079°, 40.1024°)", |
| " Salamína: (37.9643°, 23.4965°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 6573.37 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1130551.85 km²", |
| "FINAL ANSWER: Area: 1130551.85 km², Perimeter: 6573.37 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 16.85438, |
| "lon": 74.56417, |
| "name": "Sāngli" |
| }, |
| { |
| "lat": 20.81214, |
| "lon": 72.99811, |
| "name": "Gandevi" |
| }, |
| { |
| "lat": 17.45081, |
| "lon": 78.68366, |
| "name": "Ghatkesar" |
| }, |
| { |
| "lat": 10.78974, |
| "lon": 76.21898, |
| "name": "Ongallur-II" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 255985.25, |
| "perimeter_km": 2658.85, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Sāngli: (16.8544°, 74.5642°)", |
| " Gandevi: (20.8121°, 72.9981°)", |
| " Ghatkesar: (17.4508°, 78.6837°)", |
| " Ongallur-II: (10.7897°, 76.2190°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2658.85 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 255985.25 km²", |
| "FINAL ANSWER: Area: 255985.25 km², Perimeter: 2658.85 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 13.31536, |
| "lon": 12.61135, |
| "name": "Diffa" |
| }, |
| { |
| "lat": 13.47481, |
| "lon": 22.45744, |
| "name": "El Geneina Fort" |
| }, |
| { |
| "lat": 1.35639, |
| "lon": 31.22222, |
| "name": "Kikube" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 719667.98, |
| "perimeter_km": 5164.46, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Diffa: (13.3154°, 12.6113°)", |
| " El Geneina Fort: (13.4748°, 22.4574°)", |
| " Kikube: (1.3564°, 31.2222°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5164.46 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 719667.98 km²", |
| "FINAL ANSWER: Area: 719667.98 km², Perimeter: 5164.46 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": -11.60389, |
| "lon": -38.58313, |
| "name": "Sátiro Dias" |
| }, |
| { |
| "lat": -14.06694, |
| "lon": -39.64056, |
| "name": "Ibirataia" |
| }, |
| { |
| "lat": -10.46139, |
| "lon": -40.18944, |
| "name": "Senhor do Bonfim" |
| }, |
| { |
| "lat": -3.60722, |
| "lon": -38.96833, |
| "name": "São Gonçalo do Amarante" |
| }, |
| { |
| "lat": -4.45194, |
| "lon": -37.79722, |
| "name": "Fortim" |
| }, |
| { |
| "lat": -6.96596, |
| "lon": -35.7951, |
| "name": "Remígio" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 262515.9, |
| "perimeter_km": 2592.74, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Sátiro Dias: (-11.6039°, -38.5831°)", |
| " Ibirataia: (-14.0669°, -39.6406°)", |
| " Senhor do Bonfim: (-10.4614°, -40.1894°)", |
| " São Gonçalo do Amarante: (-3.6072°, -38.9683°)", |
| " Fortim: (-4.4519°, -37.7972°)", |
| " Remígio: (-6.9660°, -35.7951°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2592.74 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 262515.90 km²", |
| "FINAL ANSWER: Area: 262515.90 km², Perimeter: 2592.74 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": -24.50944, |
| "lon": -48.8425, |
| "name": "Apiaí" |
| }, |
| { |
| "lat": -20.33944, |
| "lon": -47.78056, |
| "name": "Ituverava" |
| }, |
| { |
| "lat": -16.3575, |
| "lon": -46.90611, |
| "name": "Unaí" |
| }, |
| { |
| "lat": -15.56833, |
| "lon": -40.42306, |
| "name": "Macarani" |
| }, |
| { |
| "lat": -21.55139, |
| "lon": -45.43028, |
| "name": "Varginha" |
| }, |
| { |
| "lat": -22.55417, |
| "lon": -45.78, |
| "name": "Paraisópolis" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 348398.95, |
| "perimeter_km": 2973.86, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Apiaí: (-24.5094°, -48.8425°)", |
| " Ituverava: (-20.3394°, -47.7806°)", |
| " Unaí: (-16.3575°, -46.9061°)", |
| " Macarani: (-15.5683°, -40.4231°)", |
| " Varginha: (-21.5514°, -45.4303°)", |
| " Paraisópolis: (-22.5542°, -45.7800°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2973.86 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 348398.95 km²", |
| "FINAL ANSWER: Area: 348398.95 km², Perimeter: 2973.86 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 42.50779, |
| "lon": 1.52109, |
| "name": "Andorra la Vella" |
| }, |
| { |
| "lat": 36.92077, |
| "lon": -6.07529, |
| "name": "Lebrija" |
| }, |
| { |
| "lat": 53.39234, |
| "lon": -2.63994, |
| "name": "Great Sankey" |
| }, |
| { |
| "lat": 48.69676, |
| "lon": 8.13523, |
| "name": "Bühl" |
| }, |
| { |
| "lat": 48.16783, |
| "lon": 8.62719, |
| "name": "Rottweil" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 919603.62, |
| "perimeter_km": 4571.78, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Andorra la Vella: (42.5078°, 1.5211°)", |
| " Lebrija: (36.9208°, -6.0753°)", |
| " Great Sankey: (53.3923°, -2.6399°)", |
| " Bühl: (48.6968°, 8.1352°)", |
| " Rottweil: (48.1678°, 8.6272°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4571.78 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 919603.62 km²", |
| "FINAL ANSWER: Area: 919603.62 km², Perimeter: 4571.78 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 33.88758, |
| "lon": -6.96807, |
| "name": "Aïn Attig" |
| }, |
| { |
| "lat": 35.09579, |
| "lon": -1.85772, |
| "name": "Ghazaouet" |
| }, |
| { |
| "lat": 35.16813, |
| "lon": -2.93352, |
| "name": "Nador" |
| }, |
| { |
| "lat": 35.39137, |
| "lon": -1.09238, |
| "name": "El Malah" |
| }, |
| { |
| "lat": 36.57861, |
| "lon": 10.85861, |
| "name": "Korba" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 41630.11, |
| "perimeter_km": 3480.96, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Aïn Attig: (33.8876°, -6.9681°)", |
| " Ghazaouet: (35.0958°, -1.8577°)", |
| " Nador: (35.1681°, -2.9335°)", |
| " El Malah: (35.3914°, -1.0924°)", |
| " Korba: (36.5786°, 10.8586°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3480.96 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 41630.11 km²", |
| "FINAL ANSWER: Area: 41630.11 km², Perimeter: 3480.96 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 34.80194, |
| "lon": 10.76361, |
| "name": "Sakiet ez Zit" |
| }, |
| { |
| "lat": 30.97225, |
| "lon": 30.95614, |
| "name": "Quţūr" |
| }, |
| { |
| "lat": 30.03, |
| "lon": 31.47, |
| "name": "New Cairo" |
| }, |
| { |
| "lat": 28.31214, |
| "lon": 30.71007, |
| "name": "Samālūţ" |
| }, |
| { |
| "lat": 27.3126, |
| "lon": 30.96987, |
| "name": "Manfalūţ" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 379732.41, |
| "perimeter_km": 4456.03, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Sakiet ez Zit: (34.8019°, 10.7636°)", |
| " Quţūr: (30.9722°, 30.9561°)", |
| " New Cairo: (30.0300°, 31.4700°)", |
| " Samālūţ: (28.3121°, 30.7101°)", |
| " Manfalūţ: (27.3126°, 30.9699°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4456.03 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 379732.41 km²", |
| "FINAL ANSWER: Area: 379732.41 km², Perimeter: 4456.03 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 32.96179, |
| "lon": -96.82917, |
| "name": "Addison" |
| }, |
| { |
| "lat": 33.40539, |
| "lon": -86.81138, |
| "name": "Hoover" |
| }, |
| { |
| "lat": 29.99409, |
| "lon": -90.24174, |
| "name": "Kenner" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 173853.28, |
| "perimeter_km": 2138.63, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Addison: (32.9618°, -96.8292°)", |
| " Hoover: (33.4054°, -86.8114°)", |
| " Kenner: (29.9941°, -90.2417°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2138.63 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 173853.28 km²", |
| "FINAL ANSWER: Area: 173853.28 km², Perimeter: 2138.63 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": -37.76667, |
| "lon": 144.96667, |
| "name": "Brunswick" |
| }, |
| { |
| "lat": -26.65682, |
| "lon": 153.07955, |
| "name": "Sunshine Coast" |
| }, |
| { |
| "lat": -32.92953, |
| "lon": 151.7801, |
| "name": "Newcastle" |
| }, |
| { |
| "lat": -33.88096, |
| "lon": 151.07986, |
| "name": "Strathfield" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 187263.88, |
| "perimeter_km": 2983.52, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Brunswick: (-37.7667°, 144.9667°)", |
| " Sunshine Coast: (-26.6568°, 153.0796°)", |
| " Newcastle: (-32.9295°, 151.7801°)", |
| " Strathfield: (-33.8810°, 151.0799°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2983.52 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 187263.88 km²", |
| "FINAL ANSWER: Area: 187263.88 km², Perimeter: 2983.52 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": -37.8149, |
| "lon": 144.95052, |
| "name": "Docklands" |
| }, |
| { |
| "lat": -38.02388, |
| "lon": 144.40617, |
| "name": "Lara" |
| }, |
| { |
| "lat": -36.38047, |
| "lon": 145.39867, |
| "name": "Shepparton" |
| }, |
| { |
| "lat": -28.11694, |
| "lon": 153.46584, |
| "name": "Palm Beach" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 49331.32, |
| "perimeter_km": 2784.41, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Docklands: (-37.8149°, 144.9505°)", |
| " Lara: (-38.0239°, 144.4062°)", |
| " Shepparton: (-36.3805°, 145.3987°)", |
| " Palm Beach: (-28.1169°, 153.4658°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2784.41 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 49331.32 km²", |
| "FINAL ANSWER: Area: 49331.32 km², Perimeter: 2784.41 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": 30.67307, |
| "lon": -8.18087, |
| "name": "Aoulouz" |
| }, |
| { |
| "lat": 34.30494, |
| "lon": -6.30404, |
| "name": "Sidi Yahia El Gharb" |
| }, |
| { |
| "lat": 35.00044, |
| "lon": -5.90378, |
| "name": "Ksar El Kebir" |
| }, |
| { |
| "lat": 36.12232, |
| "lon": 0.89865, |
| "name": "Mazouna" |
| }, |
| { |
| "lat": 33.35495, |
| "lon": 10.50548, |
| "name": "Medenine" |
| }, |
| { |
| "lat": 32.49094, |
| "lon": 3.67347, |
| "name": "Ghardaïa" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 523188.9, |
| "perimeter_km": 3868.54, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Aoulouz: (30.6731°, -8.1809°)", |
| " Sidi Yahia El Gharb: (34.3049°, -6.3040°)", |
| " Ksar El Kebir: (35.0004°, -5.9038°)", |
| " Mazouna: (36.1223°, 0.8986°)", |
| " Medenine: (33.3550°, 10.5055°)", |
| " Ghardaïa: (32.4909°, 3.6735°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3868.54 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 523188.90 km²", |
| "FINAL ANSWER: Area: 523188.90 km², Perimeter: 3868.54 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": -26.53333, |
| "lon": 29.06667, |
| "name": "eMbalenhle" |
| }, |
| { |
| "lat": -25.509, |
| "lon": 28.064, |
| "name": "Mabopane" |
| }, |
| { |
| "lat": -20.4943, |
| "lon": 27.03479, |
| "name": "Tutume" |
| }, |
| { |
| "lat": -13.13701, |
| "lon": 25.00653, |
| "name": "Mufumbwe" |
| }, |
| { |
| "lat": -11.66278, |
| "lon": 39.55056, |
| "name": "Mueda" |
| }, |
| { |
| "lat": -22.0, |
| "lon": 35.31667, |
| "name": "Vilankulo" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1484359.98, |
| "perimeter_km": 5196.65, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " eMbalenhle: (-26.5333°, 29.0667°)", |
| " Mabopane: (-25.5090°, 28.0640°)", |
| " Tutume: (-20.4943°, 27.0348°)", |
| " Mufumbwe: (-13.1370°, 25.0065°)", |
| " Mueda: (-11.6628°, 39.5506°)", |
| " Vilankulo: (-22.0000°, 35.3167°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5196.65 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1484359.98 km²", |
| "FINAL ANSWER: Area: 1484359.98 km², Perimeter: 5196.65 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": -1.79008, |
| "lon": -79.28759, |
| "name": "Montalvo" |
| }, |
| { |
| "lat": 9.79029, |
| "lon": -74.78244, |
| "name": "Plato" |
| }, |
| { |
| "lat": 3.62057, |
| "lon": -75.09415, |
| "name": "Natagaima" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 150545.25, |
| "perimeter_km": 2828.87, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Montalvo: (-1.7901°, -79.2876°)", |
| " Plato: (9.7903°, -74.7824°)", |
| " Natagaima: (3.6206°, -75.0941°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2828.87 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 150545.25 km²", |
| "FINAL ANSWER: Area: 150545.25 km², Perimeter: 2828.87 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 41.18389, |
| "lon": -96.03113, |
| "name": "La Vista" |
| }, |
| { |
| "lat": 44.86219, |
| "lon": -93.53079, |
| "name": "Chanhassen" |
| }, |
| { |
| "lat": 44.38358, |
| "lon": -89.81735, |
| "name": "Wisconsin Rapids" |
| }, |
| { |
| "lat": 40.74899, |
| "lon": -74.26126, |
| "name": "South Orange" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 359851.62, |
| "perimeter_km": 3913.13, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " La Vista: (41.1839°, -96.0311°)", |
| " Chanhassen: (44.8622°, -93.5308°)", |
| " Wisconsin Rapids: (44.3836°, -89.8174°)", |
| " South Orange: (40.7490°, -74.2613°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3913.13 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 359851.62 km²", |
| "FINAL ANSWER: Area: 359851.62 km², Perimeter: 3913.13 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 40.32605, |
| "lon": -3.51089, |
| "name": "Rivas-Vaciamadrid" |
| }, |
| { |
| "lat": 40.28106, |
| "lon": -7.50504, |
| "name": "Covilhã" |
| }, |
| { |
| "lat": 52.33964, |
| "lon": 4.96256, |
| "name": "Diemen" |
| }, |
| { |
| "lat": 51.83167, |
| "lon": 4.6875, |
| "name": "Papendrecht" |
| }, |
| { |
| "lat": 50.89559, |
| "lon": 7.18175, |
| "name": "Rösrath" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 386181.35, |
| "perimeter_km": 3679.59, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Rivas-Vaciamadrid: (40.3261°, -3.5109°)", |
| " Covilhã: (40.2811°, -7.5050°)", |
| " Diemen: (52.3396°, 4.9626°)", |
| " Papendrecht: (51.8317°, 4.6875°)", |
| " Rösrath: (50.8956°, 7.1818°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3679.59 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 386181.35 km²", |
| "FINAL ANSWER: Area: 386181.35 km², Perimeter: 3679.59 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": 36.13968, |
| "lon": -120.36015, |
| "name": "Coalinga" |
| }, |
| { |
| "lat": 40.56217, |
| "lon": -111.92966, |
| "name": "South Jordan" |
| }, |
| { |
| "lat": 47.86602, |
| "lon": -122.1551, |
| "name": "Silver Firs" |
| }, |
| { |
| "lat": 38.9556, |
| "lon": -90.18678, |
| "name": "Godfrey" |
| }, |
| { |
| "lat": 40.01499, |
| "lon": -105.27055, |
| "name": "Boulder" |
| }, |
| { |
| "lat": 39.37221, |
| "lon": -104.85609, |
| "name": "Castle Rock" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 2518898.03, |
| "perimeter_km": 7559.99, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Coalinga: (36.1397°, -120.3602°)", |
| " South Jordan: (40.5622°, -111.9297°)", |
| " Silver Firs: (47.8660°, -122.1551°)", |
| " Godfrey: (38.9556°, -90.1868°)", |
| " Boulder: (40.0150°, -105.2706°)", |
| " Castle Rock: (39.3722°, -104.8561°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 7559.99 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 2518898.03 km²", |
| "FINAL ANSWER: Area: 2518898.03 km², Perimeter: 7559.99 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 38.34517, |
| "lon": -0.48149, |
| "name": "Alicante" |
| }, |
| { |
| "lat": 40.37846, |
| "lon": -3.6739, |
| "name": "Entrevías" |
| }, |
| { |
| "lat": 53.50291, |
| "lon": -1.3458, |
| "name": "Wath upon Dearne" |
| }, |
| { |
| "lat": 50.85568, |
| "lon": 0.58009, |
| "name": "Hastings" |
| }, |
| { |
| "lat": 52.01954, |
| "lon": 4.42946, |
| "name": "Pijnacker" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 502804.79, |
| "perimeter_km": 4011.72, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Alicante: (38.3452°, -0.4815°)", |
| " Entrevías: (40.3785°, -3.6739°)", |
| " Wath upon Dearne: (53.5029°, -1.3458°)", |
| " Hastings: (50.8557°, 0.5801°)", |
| " Pijnacker: (52.0195°, 4.4295°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4011.72 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 502804.79 km²", |
| "FINAL ANSWER: Area: 502804.79 km², Perimeter: 4011.72 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 33.74002, |
| "lon": -116.93891, |
| "name": "East Hemet" |
| }, |
| { |
| "lat": 34.86526, |
| "lon": -120.436, |
| "name": "Orcutt" |
| }, |
| { |
| "lat": 37.72855, |
| "lon": -122.38107, |
| "name": "Bayview-Hunters Point" |
| }, |
| { |
| "lat": 32.73569, |
| "lon": -97.10807, |
| "name": "Arlington" |
| }, |
| { |
| "lat": 25.74167, |
| "lon": -100.30222, |
| "name": "San Nicolás de los Garza" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1239060.64, |
| "perimeter_km": 5731.01, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " East Hemet: (33.7400°, -116.9389°)", |
| " Orcutt: (34.8653°, -120.4360°)", |
| " Bayview-Hunters Point: (37.7285°, -122.3811°)", |
| " Arlington: (32.7357°, -97.1081°)", |
| " San Nicolás de los Garza: (25.7417°, -100.3022°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5731.01 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1239060.64 km²", |
| "FINAL ANSWER: Area: 1239060.64 km², Perimeter: 5731.01 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": -20.24056, |
| "lon": -56.37833, |
| "name": "Miranda" |
| }, |
| { |
| "lat": -23.535, |
| "lon": -47.26194, |
| "name": "Alumínio" |
| }, |
| { |
| "lat": -23.84861, |
| "lon": -50.18778, |
| "name": "Ibaiti" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 68265.78, |
| "perimeter_km": 2062.6, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Miranda: (-20.2406°, -56.3783°)", |
| " Alumínio: (-23.5350°, -47.2619°)", |
| " Ibaiti: (-23.8486°, -50.1878°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2062.60 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 68265.78 km²", |
| "FINAL ANSWER: Area: 68265.78 km², Perimeter: 2062.60 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 40.39061, |
| "lon": -3.64824, |
| "name": "Portazgo" |
| }, |
| { |
| "lat": 48.96164, |
| "lon": 10.13173, |
| "name": "Ellwangen" |
| }, |
| { |
| "lat": 46.38318, |
| "lon": 6.23955, |
| "name": "Nyon" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 35667.56, |
| "perimeter_km": 2891.32, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Portazgo: (40.3906°, -3.6482°)", |
| " Ellwangen: (48.9616°, 10.1317°)", |
| " Nyon: (46.3832°, 6.2396°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 2891.32 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 35667.56 km²", |
| "FINAL ANSWER: Area: 35667.56 km², Perimeter: 2891.32 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "5-sided", |
| "vertices": [ |
| { |
| "lat": 32.43501, |
| "lon": 13.6332, |
| "name": "Tarhuna" |
| }, |
| { |
| "lat": 31.19688, |
| "lon": 31.5243, |
| "name": "Shirbīn" |
| }, |
| { |
| "lat": 30.15293, |
| "lon": 31.31501, |
| "name": "Al Khuşūş" |
| }, |
| { |
| "lat": 25.87198, |
| "lon": 32.75585, |
| "name": "Jarājūs" |
| }, |
| { |
| "lat": 19.61745, |
| "lon": 37.21644, |
| "name": "Port Sudan" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 888228.52, |
| "perimeter_km": 5884.54, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (5 vertices)", |
| " Tarhuna: (32.4350°, 13.6332°)", |
| " Shirbīn: (31.1969°, 31.5243°)", |
| " Al Khuşūş: (30.1529°, 31.3150°)", |
| " Jarājūs: (25.8720°, 32.7559°)", |
| " Port Sudan: (19.6175°, 37.2164°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 5884.54 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 888228.52 km²", |
| "FINAL ANSWER: Area: 888228.52 km², Perimeter: 5884.54 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 38.67851, |
| "lon": -121.22578, |
| "name": "Orangevale" |
| }, |
| { |
| "lat": 45.53929, |
| "lon": -122.38731, |
| "name": "Troutdale" |
| }, |
| { |
| "lat": 31.30862, |
| "lon": -110.94217, |
| "name": "Nogales" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 341436.34, |
| "perimeter_km": 3877.95, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " Orangevale: (38.6785°, -121.2258°)", |
| " Troutdale: (45.5393°, -122.3873°)", |
| " Nogales: (31.3086°, -110.9422°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3877.95 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 341436.34 km²", |
| "FINAL ANSWER: Area: 341436.34 km², Perimeter: 3877.95 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": 33.24528, |
| "lon": 131.69165, |
| "name": "Tsurusaki" |
| }, |
| { |
| "lat": 31.42813, |
| "lon": 119.48353, |
| "name": "Licheng" |
| }, |
| { |
| "lat": 40.04068, |
| "lon": 124.33525, |
| "name": "Langtoucun" |
| }, |
| { |
| "lat": 38.70882, |
| "lon": 141.15578, |
| "name": "Tome" |
| }, |
| { |
| "lat": 35.67452, |
| "lon": 139.48216, |
| "name": "Fuchū" |
| }, |
| { |
| "lat": 34.86437, |
| "lon": 134.552, |
| "name": "Tatsunochō-tominaga" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1149238.92, |
| "perimeter_km": 4811.82, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Tsurusaki: (33.2453°, 131.6917°)", |
| " Licheng: (31.4281°, 119.4835°)", |
| " Langtoucun: (40.0407°, 124.3353°)", |
| " Tome: (38.7088°, 141.1558°)", |
| " Fuchū: (35.6745°, 139.4822°)", |
| " Tatsunochō-tominaga: (34.8644°, 134.5520°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4811.82 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1149238.92 km²", |
| "FINAL ANSWER: Area: 1149238.92 km², Perimeter: 4811.82 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "4-sided", |
| "vertices": [ |
| { |
| "lat": 43.53692, |
| "lon": 6.46458, |
| "name": "Draguignan" |
| }, |
| { |
| "lat": 49.92139, |
| "lon": 8.48255, |
| "name": "Groß-Gerau" |
| }, |
| { |
| "lat": 53.48097, |
| "lon": -2.24555, |
| "name": "Manchester City Centre" |
| }, |
| { |
| "lat": 50.91741, |
| "lon": 34.79906, |
| "name": "Sumy" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1753884.32, |
| "perimeter_km": 6349.87, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (4 vertices)", |
| " Draguignan: (43.5369°, 6.4646°)", |
| " Groß-Gerau: (49.9214°, 8.4825°)", |
| " Manchester City Centre: (53.4810°, -2.2456°)", |
| " Sumy: (50.9174°, 34.7991°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 6349.87 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1753884.32 km²", |
| "FINAL ANSWER: Area: 1753884.32 km², Perimeter: 6349.87 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "6-sided", |
| "vertices": [ |
| { |
| "lat": -9.78333, |
| "lon": 16.43333, |
| "name": "Cangandala" |
| }, |
| { |
| "lat": -8.57848, |
| "lon": 13.66425, |
| "name": "Caxito" |
| }, |
| { |
| "lat": -5.83861, |
| "lon": 13.46306, |
| "name": "Matadi" |
| }, |
| { |
| "lat": 6.32229, |
| "lon": 19.07922, |
| "name": "Dekoa" |
| }, |
| { |
| "lat": -6.22149, |
| "lon": 23.39254, |
| "name": "Miabi" |
| }, |
| { |
| "lat": -8.23619, |
| "lon": 19.52566, |
| "name": "Cuilo" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 1038628.62, |
| "perimeter_km": 4463.74, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (6 vertices)", |
| " Cangandala: (-9.7833°, 16.4333°)", |
| " Caxito: (-8.5785°, 13.6642°)", |
| " Matadi: (-5.8386°, 13.4631°)", |
| " Dekoa: (6.3223°, 19.0792°)", |
| " Miabi: (-6.2215°, 23.3925°)", |
| " Cuilo: (-8.2362°, 19.5257°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 4463.74 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 1038628.62 km²", |
| "FINAL ANSWER: Area: 1038628.62 km², Perimeter: 4463.74 km" |
| ] |
| }, |
| { |
| "task": "area_perimeter", |
| "polygon_type": "3-sided", |
| "vertices": [ |
| { |
| "lat": 32.57286, |
| "lon": -6.01947, |
| "name": "El Ksiba" |
| }, |
| { |
| "lat": 36.65393, |
| "lon": 3.98143, |
| "name": "Tirmitine" |
| }, |
| { |
| "lat": 36.82657, |
| "lon": 10.08974, |
| "name": "Douar Hicher" |
| } |
| ], |
| "ground_truth": { |
| "area_km2": 93872.72, |
| "perimeter_km": 3109.81, |
| "tolerance_percent": 5.0 |
| }, |
| "reasoning_steps": [ |
| "Step 1: Identify polygon vertices (3 vertices)", |
| " El Ksiba: (32.5729°, -6.0195°)", |
| " Tirmitine: (36.6539°, 3.9814°)", |
| " Douar Hicher: (36.8266°, 10.0897°)", |
| "Step 2: Calculate perimeter", |
| " Sum distances between consecutive vertices using Haversine", |
| " Perimeter = 3109.81 km", |
| "Step 3: Calculate area using spherical excess formula", |
| " Area on sphere = R² × E, where E is spherical excess", |
| " Area = 93872.72 km²", |
| "FINAL ANSWER: Area: 93872.72 km², Perimeter: 3109.81 km" |
| ] |
| } |
| ] |
